list of np-complete problems

7/29/2019 List of NP-Complete problems

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List of NP-complete problemsFrom Wikipedia, the free encyclopedia

Here are some of the more commonly known problems that are NP-complete when expressed as decision

problems. This list is in no way comprehensive (there are more than 3000[citation needed] known NP-complete

problems). Most of the problems in this list are taken from Garey and Johnson's seminal book Computers and

Intractability: A Guide to the Theory of NP-Completeness, and are here presented in the same order andorganization.

This is an incomplete list, which may never be able to satisfy particular standards for

completeness. You can help by expanding it (//en.wikipedia.org/w/index.php?title=List_of_NP-

complete_problems&action=edit) with reliably sourced entries.

Contents

1 Graph theory

1.1 Covering and partitioning

1.2 Subgraphs and supergraphs

1.3 Vertex ordering

1.4 Iso- and other morphisms

1.5 Miscellaneous

2 Network design

2.1 Spanning trees

2.2 Cuts and connectivity

2.3 Routing problems

2.4 Flow problems

2.5 Miscellaneous

2.6 Graph Drawing

3 Sets and partitions

3.1 Covering, hitting, and splitting

3.2 Weighted set problems

3.3 Set partitions

4 Storage and retrieval

4.1 Data storage4.2 Compression and representation

4.3 Database problems

5 Sequencing and scheduling

5.1 Sequencing on one processor

5.2 Multiprocessor scheduling

5.3 Shop scheduling

5.4 Miscellaneous

6 Mathematical programming

7 Algebra and number theory7.1 Divisibility problems

7.2 Solvability of equations

7.3 Miscellaneous

8 Games and puzzles
http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_4http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Divisibility_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Algebra_and_number_theoryhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_3http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Shop_schedulinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Sequencing_and_schedulinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Database_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Data_storagehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_2http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Flow_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Routing_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Cuts_and_connectivityhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Network_designhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneoushttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Iso-_and_other_morphismshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Vertex_orderinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Covering_and_partitioninghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Graph_theoryhttp://en.wikipedia.org/w/index.php?title=List_of_NP-complete_problems&action=edithttp://en.wikipedia.org/wiki/Wikipedia:WikiProject_Lists#Incomplete_listshttp://en.wikipedia.org/wiki/Decision_problemhttp://en.wikipedia.org/wiki/Decision_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Games_and_puzzleshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_4http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Solvability_of_equationshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Divisibility_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Algebra_and_number_theoryhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Mathematical_programminghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_3http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Shop_schedulinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Multiprocessor_schedulinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Sequencing_on_one_processorhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Sequencing_and_schedulinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Database_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Compression_and_representationhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Data_storagehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Storage_and_retrievalhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Set_partitionshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Weighted_set_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Covering.2C_hitting.2C_and_splittinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Sets_and_partitionshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Graph_Drawinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_2http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Flow_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Routing_problemshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Cuts_and_connectivityhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Spanning_treeshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Network_designhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneoushttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Iso-_and_other_morphismshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Vertex_orderinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Subgraphs_and_supergraphshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Covering_and_partitioninghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Graph_theoryhttp://en.wikipedia.org/wiki/Wikipedia:Identifying_reliable_sourceshttp://en.wikipedia.org/w/index.php?title=List_of_NP-complete_problems&action=edithttp://en.wikipedia.org/wiki/Wikipedia:WikiProject_Lists#Incomplete_listshttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Decision_problemhttp://en.wikipedia.org/wiki/NP-complete


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9 Logic

9.1 Propositional logic

9.2 Miscellaneous

10 Automata and language theory

10.1 Automata theory

10.2 Formal languages

11 Computational geometry

12 Program optimization12.1 Code generation

12.2 Programs and schemes

13 Miscellaneous

14 See also

15 Notes

16 References

Graph theory

Covering and partitioning

Vertex cover[1][2]

Dominating set, a.k.a. domination number[3]

NP-complete special cases include the edge dominating set problem, i.e., the dominating set

problem in line graphs. NP-complete variants include the connected dominating set problem.

Domatic partition, a.k.a. domatic number[4]

Graph coloring, a.k.a. chromatic number[1][5]

Partition into cliques

This is the same problem as coloring the complement of the given graph. [6]

Complete coloring, a.k.a. achromatic number[7]

Monochromatic triangle[8]

Feedback vertex set[1][9]

Feedback arc set[1][10]

Partial feedback edge set[11]

Minimum maximal independent set a.k.a. minimum independent dominating set[12]

NP-complete special cases include the minimum maximal matching problem,[13] which is essentially

equal to the edge dominating set problem (see above).

Partition into triangles[14]

Partition into isomorphic subgraphs[15]

Partition into Hamiltonian subgraphs[16]

Partition into forests[17]

Partition into perfect matchings[18]
http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-18http://en.wikipedia.org/wiki/Perfect_matchinghttp://en.wikipedia.org/wiki/Graph_partitionhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-17http://en.wikipedia.org/wiki/Forest_(graph_theory)http://en.wikipedia.org/wiki/Graph_partitionhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-16http://en.wikipedia.org/wiki/Glossary_of_graph_theory#Subgraphshttp://en.wikipedia.org/wiki/Hamiltonian_graphhttp://en.wikipedia.org/wiki/Graph_partitionhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-15http://en.wikipedia.org/wiki/Glossary_of_graph_theory#Subgraphshttp://en.wikipedia.org/wiki/Graph_isomorphismhttp://en.wikipedia.org/wiki/Graph_partitionhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-14http://en.wikipedia.org/wiki/Graph_partitionhttp://en.wikipedia.org/wiki/Edge_dominating_sethttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-13http://en.wikipedia.org/wiki/Minimum_maximal_matchinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-12http://en.wikipedia.org/wiki/Minimum_maximal_independent_sethttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-11http://en.wikipedia.org/w/index.php?title=Partial_feedback_edge_set&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-10http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Feedback_arc_sethttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-9http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Feedback_vertex_sethttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-8http://en.wikipedia.org/wiki/Monochromatic_trianglehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-7http://en.wikipedia.org/wiki/Complete_coloringhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-6http://en.wikipedia.org/wiki/Complement_(graph_theory)http://en.wikipedia.org/wiki/Graph_coloringhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-5http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Graph_coloringhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-4http://en.wikipedia.org/wiki/Domatic_partitionhttp://en.wikipedia.org/wiki/Connected_dominating_sethttp://en.wikipedia.org/wiki/Edge_dominating_sethttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-3http://en.wikipedia.org/wiki/Dominating_set_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-2http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Vertex_coverhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Referenceshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Noteshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#See_alsohttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_6http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Programs_and_schemeshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Code_generationhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Program_optimizationhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Computational_geometryhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Formal_languageshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Automata_theoryhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Automata_and_language_theoryhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Miscellaneous_5http://en.wikipedia.org/wiki/List_of_NP-complete_problems#Propositional_logichttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#Logic


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Two-stage maximum weight stochastic matching[citation needed]

Clique covering problem[1][19]

Berth allocation problem[citation needed]

Covering by complete bipartite subgraphs[20]

Grundy number[21]

Rank coloring a.k.a. cycle rank

Treewidth

[22]

Subgraphs and supergraphs

Clique[1][23]

Independent set[24]

Induced subgraph with property [citation needed]]]

Induced connected subgraph with property [citation needed]]]

Induced path[25]

Balanced complete bipartite subgraph[26]Bipartite subgraph[27]

Degree-bounded connected subgraph[28]

Planar subgraph[29]

Edge-subgraph[30]

Transitive subgraph[31]

Uniconnected subgraph[32]

Minimum k-connected subgraph[33]

Cubic subgraph[34]

Minimum equivalent digraph[35]

Hamiltonian completion[36]

Interval graph completion[37]

Path graph completion[38]

Vertex ordering

Hamiltonian circuit[1][39]

Directed Hamiltonian circuit[1][40]

Hamiltonian path[41]

Bandwidth[42]

Directed bandwidth[43]

Optimal linear arrangement[44]

Directed optimal linear arrangement[45]

Minimum cut linear arrangement[46]

Rooted tree arrangement[47]

Directed elimination ordering[48]

Elimination degree sequence[49]

Pathwidth,[22] or, equivalently, interval thickness, and vertex separation number[50]

Iso- and other morphisms
http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-50http://en.wikipedia.org/wiki/Path_decomposition#Vertex_separation_numberhttp://en.wikipedia.org/wiki/Path_decomposition#Interval_thicknesshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-acp1987-22http://en.wikipedia.org/wiki/Pathwidthhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-49http://en.wikipedia.org/w/index.php?title=Elimination_degree_sequence&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-48http://en.wikipedia.org/w/index.php?title=Directed_elimination_ordering&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-47http://en.wikipedia.org/w/index.php?title=Rooted_tree_arrangement&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-46http://en.wikipedia.org/w/index.php?title=Minimum_cut_linear_arrangement&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-45http://en.wikipedia.org/w/index.php?title=Directed_optimal_linear_arrangement&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-44http://en.wikipedia.org/w/index.php?title=Optimal_linear_arrangement&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-43http://en.wikipedia.org/w/index.php?title=Directed_bandwidth&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-42http://en.wikipedia.org/wiki/Bandwidth_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-41http://en.wikipedia.org/wiki/Hamiltonian_path_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-40http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Directed_Hamiltonian_circuit_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-39http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Hamiltonian_path_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-38http://en.wikipedia.org/w/index.php?title=Path_graph_completion&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-37http://en.wikipedia.org/w/index.php?title=Interval_graph_completion&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-36http://en.wikipedia.org/wiki/Hamiltonian_completionhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-35http://en.wikipedia.org/w/index.php?title=Minimum_equivalent_digraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-34http://en.wikipedia.org/w/index.php?title=Cubic_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-33http://en.wikipedia.org/w/index.php?title=Minimum_k-connected_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-32http://en.wikipedia.org/w/index.php?title=Uniconnected_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-31http://en.wikipedia.org/w/index.php?title=Transitive_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-30http://en.wikipedia.org/w/index.php?title=Edge-subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-29http://en.wikipedia.org/w/index.php?title=Planar_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-28http://en.wikipedia.org/w/index.php?title=Degree-bounded_connected_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-27http://en.wikipedia.org/wiki/Bipartite_subgraphhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-26http://en.wikipedia.org/w/index.php?title=Balanced_complete_bipartite_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-25http://en.wikipedia.org/wiki/Induced_pathhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/w/index.php?title=Property_%CE%A0&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Induced_connected_subgraph&action=edit&redlink=1http://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/w/index.php?title=Property_%CE%A0&action=edit&redlink=1http://en.wikipedia.org/wiki/Induced_subgraphhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-24http://en.wikipedia.org/wiki/Independent_set_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-23http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Clique_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-acp1987-22http://en.wikipedia.org/wiki/Treewidthhttp://en.wikipedia.org/wiki/Cycle_rankhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-.7B.7Bharvtxt.7CGarey.7CJohnson.7C1979.7D.7D:_GT56-21http://en.wikipedia.org/wiki/Grundy_numberhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-20http://en.wikipedia.org/wiki/Bipartite_dimensionhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Berth_allocation_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-19http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Clique_coverhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/w/index.php?title=Stochastic_matching&action=edit&redlink=1


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Subgraph isomorphism[51]

Largest common subgraph[52]

Maximum subgraph matching[53]

Graph contractibility[54]

Graph homomorphism[55]

Digraph D-morphism[56]

Miscellaneous

Path with forbidden pairs[57]

Multiple choice matching[58]

Graph Grundy numbering[21]

Kernel[59]

K-closure[60]

Intersection graph basis[61]

Path distinguishers[62]

Metric dimension[63]

NeetilRdl dimension[64]

Threshold number[65]

Oriented diameter[66]

Weighted diameter[67]

Network design

Spanning trees

Degree-constrained spanning tree

Minimum degree spanning tree

Maximum leaf spanning tree

Minimum k-spanning tree

Shortest total path length spanning tree

Bounded diameter spanning tree

Capacitated spanning tree

Geometric capacitated spanning tree

Optimum communication spanning tree

Isomorphic spanning tree

Kth best spanning tree

Bounded component spanning forest

Multiple choice branching

Steiner tree[1]

Geometric Steiner tree

Cable Trench Problem

Minimum touching tree/Minimum length corridor

Cuts and connectivity
http://en.wikipedia.org/w/index.php?title=Minimum_length_corridor&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Minimum_touching_tree&action=edit&redlink=1http://en.wikipedia.org/wiki/Steiner_treehttp://en.wikipedia.org/wiki/Steiner_treehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Steiner_treehttp://en.wikipedia.org/w/index.php?title=Multiple_choice_branching&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Bounded_component_spanning_forest&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Kth_best_spanning_tree&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Isomorphic_spanning_tree&action=edit&redlink=1http://en.wikipedia.org/wiki/Steiner_treehttp://en.wikipedia.org/w/index.php?title=Geometric_capacitated_spanning_tree&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Capacitated_spanning_tree&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Bounded_diameter_spanning_tree&action=edit&redlink=1http://en.wikipedia.org/wiki/Shortest_total_path_length_spanning_treehttp://en.wikipedia.org/wiki/Minimum_k-spanning_treehttp://en.wikipedia.org/wiki/Maximum_leaf_spanning_treehttp://en.wikipedia.org/wiki/Minimum_degree_spanning_treehttp://en.wikipedia.org/wiki/Degree-constrained_spanning_treehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-67http://en.wikipedia.org/w/index.php?title=Weighted_diameter&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-66http://en.wikipedia.org/w/index.php?title=Oriented_diameter&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-65http://en.wikipedia.org/w/index.php?title=Threshold_number&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-64http://en.wikipedia.org/w/index.php?title=Ne%C5%A1et%C5%99il%E2%80%93R%C3%B6dl_dimension&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-63http://en.wikipedia.org/wiki/Metric_dimension_(graph_theory)http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-62http://en.wikipedia.org/w/index.php?title=Path_distinguishers&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-61http://en.wikipedia.org/wiki/Intersection_graph_basishttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-60http://en.wikipedia.org/w/index.php?title=K-closure&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-59http://en.wikipedia.org/w/index.php?title=Kernel_problem&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-.7B.7Bharvtxt.7CGarey.7CJohnson.7C1979.7D.7D:_GT56-21http://en.wikipedia.org/w/index.php?title=Graph_Grundy_numbering&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-58http://en.wikipedia.org/w/index.php?title=Multiple_choice_matching&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-57http://en.wikipedia.org/w/index.php?title=Path_with_forbidden_pairs&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-56http://en.wikipedia.org/w/index.php?title=Digraph_D-morphism&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-55http://en.wikipedia.org/wiki/Graph_homomorphismhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-54http://en.wikipedia.org/w/index.php?title=Graph_contractibility&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-53http://en.wikipedia.org/w/index.php?title=Maximum_subgraph_matching&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-52http://en.wikipedia.org/wiki/Maximum_common_subgraph_isomorphism_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-51http://en.wikipedia.org/wiki/Subgraph_isomorphism_problem


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Graph partitioning

Acyclic partition

Maximum cut[1]

Minimum bounded cut (minimum cut into bounded sets)

Biconnectivity augmentation

Strong connectivity augmentation

Network reliability

Network survivabilityNormalized cut[68]

Multiway cut

Minimum k-cut

k-vital edges

Routing problems

Bottleneck traveling salesman

Chinese postman for mixed graphsEuclidean traveling salesman

k-Chinese postman

K most vital arcs

Kth shortest path problem

Metric traveling salesman

Longest circuit problem

Longest path problem

Prize collecting traveling salesman

Rural postmanShortest path in general networks

Shortest weight-constrained path

Stacker-crane

Time constrained traveling salesman feasibility

Traveling salesman problem (decision version)

Vehicle routing problem

Capacitated arc routing problem

Flow problems

Minimum edge-cost flow

Integral flow with multipliers

Path constrained network flow

Integral flow with homologous arcs

Integral flow with bundles

Undirected flow with lower bounds

Directed two-commodity integral flow

Undirected two-commodity integral flow

Disjoint connecting pathsMaximum length-bounded disjoint paths

Maximum fixed-length disjoint paths

Maximum flow network interdiction problem
http://en.wikipedia.org/w/index.php?title=Maximum_flow_network_interdiction_problem&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maximum_fixed-length_disjoint_paths&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maximum_length-bounded_disjoint_paths&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Disjoint_connecting_paths&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Undirected_two-commodity_integral_flow&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Directed_two-commodity_integral_flow&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Undirected_flow_with_lower_bounds&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Integral_flow_with_bundles&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Integral_flow_with_homologous_arcs&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Path_constrained_network_flow&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Integral_flow_with_multipliers&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Minimum_edge-cost_flow&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Capacitated_arc_routing_problem&action=edit&redlink=1http://en.wikipedia.org/wiki/Vehicle_routing_problemhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/w/index.php?title=Time_constrained_traveling_salesman&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Stacker-crane&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Shortest_weight-constrained_path&action=edit&redlink=1http://en.wikipedia.org/wiki/Shortest_path_problemhttp://en.wikipedia.org/wiki/Route_inspection_problem#Variantshttp://en.wikipedia.org/w/index.php?title=Prize_collecting_traveling_salesman&action=edit&redlink=1http://en.wikipedia.org/wiki/Longest_path_problemhttp://en.wikipedia.org/w/index.php?title=Longest_circuit_problem&action=edit&redlink=1http://en.wikipedia.org/wiki/Metric_traveling_salesmanhttp://en.wikipedia.org/w/index.php?title=Kth_shortest_path_problem&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=K_most_vital_arcs&action=edit&redlink=1http://en.wikipedia.org/wiki/Route_inspection_problem#Variantshttp://en.wikipedia.org/wiki/Euclidean_traveling_salesmanhttp://en.wikipedia.org/wiki/Mixed_graphhttp://en.wikipedia.org/wiki/Chinese_postmanhttp://en.wikipedia.org/wiki/Bottleneck_traveling_salesmanhttp://en.wikipedia.org/w/index.php?title=K-vital_edge&action=edit&redlink=1http://en.wikipedia.org/wiki/Minimum_k-cuthttp://en.wikipedia.org/w/index.php?title=Multiway_cut&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-68http://en.wikipedia.org/w/index.php?title=Normalized_cut&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Network_survivability&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Network_reliability&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Strong_connectivity_augmentation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Biconnectivity_augmentation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Minimum_bounded_cut&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Maximum_cuthttp://en.wikipedia.org/w/index.php?title=Acyclic_partition&action=edit&redlink=1http://en.wikipedia.org/wiki/Graph_partitioning


6/17

Unsplittable multicommodity flow

Miscellaneous

Quadratic assignment problem

Minimizing dummy activities in PERT networks

Constrained triangulation

Intersection graph for segments on a gridEdge embedding on a grid

Geometric connected dominating set

Minimum broadcast time problem

Min-max multicenter

Min-sum multicenter

Uncapacitated Facility Location

Metric k-center

Graph Drawing

Graphs occur frequently in everyday applications, and are used to model a lot of often huge data. Such

examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in

some cases (see e.g. Facebook or LinkedIn). Therefore, even when all information is available in the form of a

graph, it is important to have good ways of visualizing the data in order to make sense of it and extract

interesting features, and this is what makes graph drawing important.

Rectilinear planarity testing[69]

Upward planarity testing[69]

Upward sphericity testingMaximum upward planar subgraph computation for embedded digraphs

Sets and partitions

Covering, hitting, and splitting

3-dimensional matching[1][70]

Exact cover[1][71]

Set packing[1][72]

Set splitting[73]

Set cover[1][74]

Minimum test set[75]

Set basis[76]

Hitting set[1][77]

Intersection pattern[78]

Comparative containment[79]

3-matroid intersection[80]

Weighted set problems
http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-80http://en.wikipedia.org/w/index.php?title=3-matroid_intersection&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-79http://en.wikipedia.org/w/index.php?title=Comparative_containment&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-78http://en.wikipedia.org/w/index.php?title=Intersection_pattern&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-77http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Hitting_sethttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-76http://en.wikipedia.org/wiki/Bipartite_dimensionhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-75http://en.wikipedia.org/w/index.php?title=Minimum_test_set&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-74http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Set_cover_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-73http://en.wikipedia.org/wiki/Set_splittinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-72http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Set_packinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-71http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Exact_coverhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-70http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/3-dimensional_matchinghttp://en.wikipedia.org/w/index.php?title=Embedded_digraph&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Upward_sphericity&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-Comp2Planar-69http://en.wikipedia.org/wiki/Hasse_diagram#Upward_planarityhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-Comp2Planar-69http://en.wikipedia.org/w/index.php?title=Rectilinear_planarity&action=edit&redlink=1http://en.wikipedia.org/wiki/Graph_drawinghttp://en.wikipedia.org/wiki/LinkedInhttp://en.wikipedia.org/wiki/Facebookhttp://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Metric_k-centerhttp://en.wikipedia.org/wiki/Facility_locationhttp://en.wikipedia.org/w/index.php?title=Min-sum_multicenter&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Min-max_multicenter&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Minimum_broadcast_time_problem&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Geometric_connected_dominating_set&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Edge_embedding_problem&action=edit&redlink=1http://en.wikipedia.org/wiki/Intersection_graphhttp://en.wikipedia.org/w/index.php?title=Constrained_triangulation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=PERT_networks&action=edit&redlink=1http://en.wikipedia.org/wiki/Quadratic_assignment_problemhttp://en.wikipedia.org/w/index.php?title=Unsplittable_multicommodity_flow&action=edit&redlink=1


7/17

Partition[1]

Subset sum

Subset product

3-partition

Numerical 3-dimensional matching

Numerical matching with target sums

Expected component sum

Minimum sum of squaresKth largest subset

Kth largest m-tuple

Set partitions

Median partition

Storage and retrieval

Data storage

Bin packing[81]

Dynamic storage allocation[82]

Pruned trie space minimization[83]

Expected retrieval cost[84]

Rooted tree storage assignment[85]

Multiple copy file allocation

[86]

Capacity assignment[87]

Compression and representation

Shortest common supersequence[88]

Shortest common superstring[89]

Longest common subsequence problem for the case of arbitrary (i.e., not a priori fixed) number of input

sequences. (In contrast, the alphabet size is immaterial as long as it is greater than one.)[90]

Bounded Post correspondence problem[91]

Hitting string[92]

Sparse matrix compression[93]

Consecutive ones submatrix[94]

Consecutive ones matrix partition[95]

Consecutive ones matrix augmentation[96]

Consecutive block minimization[97]

Consecutive sets[98]

2-dimensional consecutive sets[99]

String-to-string correction[100]

Grouping by swapping[101]

External macro data compression[102]

Internal macro data compression[103]
http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-103http://en.wikipedia.org/w/index.php?title=Internal_macro_data_compression&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-102http://en.wikipedia.org/w/index.php?title=External_macro_data_compression&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-101http://en.wikipedia.org/w/index.php?title=Grouping_by_swapping&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-100http://en.wikipedia.org/wiki/String-to-string_correction_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-99http://en.wikipedia.org/w/index.php?title=2-dimensional_consecutive_sets&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-98http://en.wikipedia.org/w/index.php?title=Consecutive_sets&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-97http://en.wikipedia.org/w/index.php?title=Consecutive_block_minimization&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-96http://en.wikipedia.org/w/index.php?title=Consecutive_ones_matrix_augmentation&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-95http://en.wikipedia.org/w/index.php?title=Consecutive_ones_matrix_partition&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-94http://en.wikipedia.org/w/index.php?title=Consecutive_ones_submatrix&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-93http://en.wikipedia.org/wiki/Sparse_matrixhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-92http://en.wikipedia.org/w/index.php?title=Hitting_string&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-91http://en.wikipedia.org/wiki/Bounded_Post_correspondence_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-90http://en.wikipedia.org/wiki/Longest_common_subsequence_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-89http://en.wikipedia.org/w/index.php?title=Shortest_common_superstring&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-88http://en.wikipedia.org/wiki/Shortest_common_supersequencehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-87http://en.wikipedia.org/w/index.php?title=Capacity_assignment&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-86http://en.wikipedia.org/w/index.php?title=Multiple_copy_file_allocation&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-85http://en.wikipedia.org/w/index.php?title=Rooted_tree_storage_assignment&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-84http://en.wikipedia.org/w/index.php?title=Expected_retrieval_cost&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-83http://en.wikipedia.org/w/index.php?title=Pruned_trie_space_minimization&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-82http://en.wikipedia.org/w/index.php?title=Dynamic_storage_allocation&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-81http://en.wikipedia.org/wiki/Bin_packing_problemhttp://en.wikipedia.org/w/index.php?title=Median_partition&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Kth_largest_m-tuple&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Kth_largest_subset&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Minimum_sum_of_squares&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Expected_component_sum&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Numerical_matching_with_target_sums&action=edit&redlink=1http://en.wikipedia.org/wiki/Numerical_3-dimensional_matchinghttp://en.wikipedia.org/wiki/3-partitionhttp://en.wikipedia.org/w/index.php?title=Subset_product_problem&action=edit&redlink=1http://en.wikipedia.org/wiki/Subset_sum_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Partition_problem


8/17

Regular expression substitution[104]

Rectilinear picture compression[105]

Optimal vector quantization codebook[citation needed]

Minimal grammar-based compression[citation needed]

Adaptive block-size compression[citation needed]

Database problems

Minimum cardinality key[106]

Additional key[107]

Prime attribute name[108]

Boyce-Codd normal form violation[109]

Conjunctive query foldability[110]

Conjunctive Boolean query[111]

Tableau equivalence[112]

Serializability of database histories[113]

Safety of database transaction systems[114]

Consistency of database frequency tables[115]

Safety of file protection systems[116]

Sequencing and scheduling

Sequencing on one processor

Job sequencing[1]

Sequencing with release times and deadlines

Sequencing to minimize tardy tasks

Sequencing to minimize tardy weight

Sequencing to minimize weighted completion time

Sequencing to minimize weighted tardiness

Sequencing with deadlines and set-up times

Sequencing to minimize maximum cumulative cost

Multiprocessor scheduling

Multiprocessor scheduling

Precedence constrained scheduling

Resource constrained scheduling

Scheduling with individual deadlines

Preemptive scheduling

Scheduling to minimize weighted completion time

Shop scheduling

Open-shop scheduling

Flow Shop Scheduling Problem
http://en.wikipedia.org/wiki/Flow_Shop_Scheduling_Problemhttp://en.wikipedia.org/wiki/Open-shop_schedulinghttp://en.wikipedia.org/w/index.php?title=Preemptive_scheduling&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Resource_constrained_scheduling&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Precedence_constrained_scheduling&action=edit&redlink=1http://en.wikipedia.org/wiki/Multiprocessor_schedulinghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/w/index.php?title=Job_sequencing&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-116http://en.wikipedia.org/w/index.php?title=File_protection_safety&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-115http://en.wikipedia.org/w/index.php?title=Frequency_table_consistency&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-114http://en.wikipedia.org/w/index.php?title=Database_transaction_safety&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-113http://en.wikipedia.org/wiki/Serializabilityhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-112http://en.wikipedia.org/w/index.php?title=Tableau_equivalence&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-111http://en.wikipedia.org/wiki/Conjunctive_Boolean_queryhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-110http://en.wikipedia.org/w/index.php?title=Conjunctive_query_foldability&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-109http://en.wikipedia.org/wiki/Boyce-Codd_normal_formhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-108http://en.wikipedia.org/w/index.php?title=Prime_attribute_name&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-107http://en.wikipedia.org/w/index.php?title=Additional_key&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-106http://en.wikipedia.org/w/index.php?title=Minimum_cardinality_key&action=edit&redlink=1http://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/w/index.php?title=Adaptive_block-size_compression&action=edit&redlink=1http://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/w/index.php?title=Minimal_grammar-based_compression&action=edit&redlink=1http://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/w/index.php?title=Optimal_vector_quantization_codebook&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-105http://en.wikipedia.org/w/index.php?title=Rectilinear_picture_compression&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-104http://en.wikipedia.org/w/index.php?title=Regular_expression_substitution&action=edit&redlink=1


9/17

No-wait Flow Shop Scheduling

Two-processor Flow Shop with bounded buffer

Job-shop scheduling

Miscellaneous

Timetable design

Staff schedulingProduction planning

Deadlock avoidance

Mathematical programming

Integer linear programming

0-1 linear programming[1]

Quadratic programming (NP-hard in some cases, P if convex)

Cost-parametric linear programmingFeasible basis extension

Open hemisphere

K-relevancy

Traveling salesman polytope non-adjacency

Knapsack[1]

Integer knapsack

Continuous multiple choice knapsack

Partially ordered knapsack

Generalized assignment problemComparative vector inequalities

Selecting a maximum volume submatrix Problem of selecting the best conditioned subset of a larger m x

n matrix. This class of problem is associated with Rank revealing QR factorizations and D optimal

experimental design.[117]

Sparse approximation

Algebra and number theory

Divisibility problems

Quadratic congruences

Simultaneous incongruences

Simultaneous divisibility of linear polynomials

Comparative divisibility

Exponential expression divisibility

Non-divisibility of a product polynomial

Solvability of equations

Quadratic Diophantine equations

Algebraic equations over GF(2); or over any finite field.
http://en.wikipedia.org/wiki/Finite_fieldhttp://en.wikipedia.org/wiki/GF(2)http://en.wikipedia.org/wiki/Algebraic_equationhttp://en.wikipedia.org/wiki/Diophantine_equationhttp://en.wikipedia.org/w/index.php?title=Quadratic_diophantine_equation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Product_polynomial&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Exponential_expression&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Comparative_divisibility&action=edit&redlink=1http://en.wikipedia.org/wiki/Linear_polynomialhttp://en.wikipedia.org/w/index.php?title=Polynomial_divisibility&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Simultaneous_incongruences&action=edit&redlink=1http://en.wikipedia.org/wiki/Quadratic_congruenceshttp://en.wikipedia.org/wiki/Sparse_approximationhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-117http://en.wikipedia.org/wiki/QR_factorizationhttp://en.wikipedia.org/wiki/Submatrixhttp://en.wikipedia.org/w/index.php?title=Comparative_vector_inequalities&action=edit&redlink=1http://en.wikipedia.org/wiki/Generalized_assignment_problemhttp://en.wikipedia.org/w/index.php?title=Partially_ordered_knapsack&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_knapsack_problems#Direct_generalizationshttp://en.wikipedia.org/wiki/List_of_knapsack_problems#Direct_generalizationshttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Knapsack_problemhttp://en.wikipedia.org/w/index.php?title=Traveling_salesman_polytope_non-adjacency&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=K-relevancy&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Open_hemisphere&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Feasible_basis_extension&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Cost-parametric_linear_programming&action=edit&redlink=1http://en.wikipedia.org/wiki/Quadratic_programminghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Linear_programming#Integer_unknownshttp://en.wikipedia.org/wiki/Linear_programming#Integer_unknownshttp://en.wikipedia.org/wiki/Deadlock_avoidancehttp://en.wikipedia.org/w/index.php?title=Production_planning&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Staff_scheduling&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Timetable_design&action=edit&redlink=1http://en.wikipedia.org/wiki/Job-shop_schedulinghttp://en.wikipedia.org/w/index.php?title=No-wait_Flow_Shop_Scheduling&action=edit&redlink=1


10/17

Root of modulus 1

Number of roots for a product polynomial

Periodic solution recurrence relation

Non-linear univariate polynomials over GF[2n], n the length of the input. Indeed over any GF[qn].

Miscellaneous

Cosine product integrationEquilibrium point

Unification with commutative operators

Unification for finitely presented algebras

Integer expression membership

Minimal addition chain

Games and puzzles

Alternating hitting setAlternating maximum weighted matching

Annihilation

Battleship

Bulls and Cows, marketed as Master Mind

Clickomania (SameGame)

Crossword puzzle construction

Eternity II

Fillomino[118]

Flood-It[119]

FreeCell[120]

Heyawake[121]

Instant Insanity

Kakuro (Cross Sums)

Kuromasu (also known as Kurodoko)[122]

Lemmings[123]

Light Up

Magnets[124]

Masyu[125]

Minesweeper Consistency Problem[126] (but see Scott, Stege, & van Rooij[127])

Nurikabe

Paint by numbers (Nonogram)

Rabin games

Sift

Slither Link on a variety of grids[128][129][130][131]

Square-tiling

Sudoku

Super Mario Bros[132]

Tetris

Variable partition truth assignment

Verbal arithmetic
http://en.wikipedia.org/wiki/Verbal_arithmetichttp://en.wikipedia.org/w/index.php?title=Variable_partition_truth_assignment&action=edit&redlink=1http://en.wikipedia.org/wiki/Tetrishttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-132http://en.wikipedia.org/wiki/Super_Mario_Broshttp://en.wikipedia.org/wiki/Sudokuhttp://en.wikipedia.org/w/index.php?title=Square-tiling&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-K.C3.B6lker12c-131http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-NU07-130http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-Yato03-129http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-YS03-128http://en.wikipedia.org/wiki/Slither_Linkhttp://en.wikipedia.org/w/index.php?title=Sift_(game)&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Rabin_game&action=edit&redlink=1http://en.wikipedia.org/wiki/Nonogramhttp://en.wikipedia.org/wiki/Nurikabehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-127http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-126http://en.wikipedia.org/wiki/Minesweeper_Consistency_Problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-Friedman-125http://en.wikipedia.org/wiki/Masyuhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-K.C3.B6lker12a-124http://en.wikipedia.org/w/index.php?title=Magnets_(puzzle)&action=edit&redlink=1http://en.wikipedia.org/wiki/Light_Uphttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-Cormode04-123http://en.wikipedia.org/wiki/Lemmings_(game)http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-K.C3.B6lker12b-122http://en.wikipedia.org/wiki/Kuromasuhttp://en.wikipedia.org/wiki/Kakurohttp://en.wikipedia.org/wiki/Instant_Insanityhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-Holzer-Ruepp07-121http://en.wikipedia.org/wiki/Heyawakehttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-120http://en.wikipedia.org/wiki/FreeCellhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-119http://en.wikipedia.org/w/index.php?title=Flood-It&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-118http://en.wikipedia.org/wiki/Fillominohttp://en.wikipedia.org/wiki/Eternity_II_Puzzlehttp://en.wikipedia.org/wiki/Crosswordhttp://en.wikipedia.org/wiki/SameGamehttp://en.wikipedia.org/wiki/Mastermind_(board_game)http://en.wikipedia.org/wiki/Bulls_and_Cowshttp://en.wikipedia.org/wiki/Battleship_(puzzle)http://en.wikipedia.org/w/index.php?title=Annihilation_problem&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Alternating_maximum_weighted_matching&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Alternating_hitting_set&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Minimal_addition_chain&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Integer_expression&action=edit&redlink=1http://en.wikipedia.org/wiki/Finitely_presented_algebrahttp://en.wikipedia.org/wiki/Unification_(computer_science)http://en.wikipedia.org/wiki/Commutativityhttp://en.wikipedia.org/wiki/Unification_(computer_science)http://en.wikipedia.org/w/index.php?title=Equilibrium_point_problem&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Cosine_product_integration&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Periodic_solution_recurrence_relation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Product_polynomial&action=edit&redlink=1http://en.wikipedia.org/wiki/Modulus


11/17

Logic

Propositional logic

Propositional logic problems, in particular satisfiability problems and their variants, are of particular practical

interest because many practical problems can be solved by expressing them as satisfiability problems, and then

using efficient SAT solvers to obtain an exact solution quickly[citation needed].

Boolean satisfiability[1][133]

3-satisfiability[1][134]

Not-all-equal 3SAT[135]

One-in-three 3SAT[136]

Maximum 2-Satisfiability[137]

Generalized satisfiability[138]

Non-tautology[139]

Minimum equivalent disjunctive normal form for a given truth table[140]

Truth-functionally complete connectives[141]

Planar-3SAT

Monotone-3SAT

Miscellaneous

Modal logic S5-Satisfiability

Negation-free logic

Conjunctive satisfiability with functions and inequalities

Minimum axiom set

First order subsumption

Second order instantiation

Automata and language theory

Automata theory

Reduction of incompletely specified automata[142]

Minimum inferred finite state automaton[143]

Formal languages

Minimum inferred regular expression[144]

Reynolds covering for context-free grammars[145]

Non-LR(k) context-free grammar[146]

Context-free programmed language membership[147]

Quasi-real-time language membership[148]

Computational geometry
http://en.wikipedia.org/wiki/Computational_geometryhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-148http://en.wikipedia.org/w/index.php?title=Quasi-real-time_language&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-147http://en.wikipedia.org/w/index.php?title=Context-free_programmed_language&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-146http://en.wikipedia.org/wiki/LR_parserhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-145http://en.wikipedia.org/wiki/Context-free_grammarshttp://en.wikipedia.org/w/index.php?title=Reynolds_covering&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-144http://en.wikipedia.org/w/index.php?title=Minimum_inferred_regular_expression&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-143http://en.wikipedia.org/w/index.php?title=Minimum_inferred_finite_state_automaton&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-142http://en.wikipedia.org/wiki/Universal_instantiationhttp://en.wikipedia.org/wiki/Second_order_logichttp://en.wikipedia.org/w/index.php?title=Subsumption_(logic)&action=edit&redlink=1http://en.wikipedia.org/wiki/First_order_logichttp://en.wikipedia.org/w/index.php?title=Minimum_axiom_set&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Negation-free_logic&action=edit&redlink=1http://en.wikipedia.org/wiki/Modal_logichttp://en.wikipedia.org/w/index.php?title=Monotone-3SAT&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Planar-3SAT&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-141http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-140http://en.wikipedia.org/wiki/Disjunctive_normal_formhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-139http://en.wikipedia.org/w/index.php?title=Non-tautology&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-138http://en.wikipedia.org/w/index.php?title=Generalized_satisfiability&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-137http://en.wikipedia.org/wiki/MAX-SAThttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-136http://en.wikipedia.org/wiki/One-in-three_3SAThttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-135http://en.wikipedia.org/w/index.php?title=Not-all-equal_3SAT&action=edit&redlink=1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-134http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/3-satisfiabilityhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-133http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-karp-1http://en.wikipedia.org/wiki/Boolean_satisfiabilityhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/SAT_solver


12/17

Testing whether a tree may be represented as Euclidean minimum spanning tree

Unit disk graph recognition (Unit disk graphs are intersection graphs of circles of unit radius in the

plane)[149]

Many motion planning among polygonal obstacles in the plane are NP-hard.

Planar partitioning into connected subassemblies: Given a set A of non-overlapping (but possibly

touching) polygons in the plane, decide if there is a proper subset S of A that can be separated

from A\S by a collision-free rigid motion of S, and such that both S and A\S are connected. [150]

Art gallery problem and its variations.

Program optimization

Code generation

Register sufficiency

Feasible register assignment

Register sufficiency for loops

Code generation on a one-register machine

Code generation with unlimited registers

Code generation for parallel assignments

Code generation with address expressions

Code generation with unfixed variable locations

Ensemble computation

Microcode bit optimization

Programs and schemes

Inequivalence of programs with arrays

Inequivalence of programs with assignments

Inequivalence of finite memory programs

Inequivalence of loop programs without nesting

Inequivalence of simple functions

Strong inequivalence of Ianov schemes

Strong inequivalence for monadic recursion

Non-containment for free B-schemes

Non-freedom for loop-free program schemesPrograms with formally recursive procedures

Miscellaneous

Sorting by Reversals

Sorting by Transpositions

Block Sorting (Sorting by Block Moves)

Pancake sorting

Cyclic orderingNon-liveness of free choice Petri nets

Reachability for 1-conservative Petri nets

Finite function generation

Permutation generation
http://en.wikipedia.org/w/index.php?title=Permutation_generation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Finite_function_generation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=1-conservative_Petri_net&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Free_choice_Petri_net&action=edit&redlink=1http://en.wikipedia.org/wiki/Cyclic_orderinghttp://en.wikipedia.org/wiki/Pancake_sortinghttp://en.wikipedia.org/w/index.php?title=Program_scheme&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=B-scheme&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Free_B-scheme&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Monadic_recursion&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Ianov_schemes&action=edit&redlink=1http://en.wikipedia.org/wiki/Assignment_(computer_programming)http://en.wikipedia.org/wiki/Array_data_structurehttp://en.wikipedia.org/w/index.php?title=Program_equivalence&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Microcode_bit_optimization&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Ensemble_computation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Address_expression&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Parallel_assignments&action=edit&redlink=1http://en.wikipedia.org/wiki/Processor_registerhttp://en.wikipedia.org/wiki/Code_generationhttp://en.wikipedia.org/w/index.php?title=Feasible_register_assignment&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Register_sufficiency&action=edit&redlink=1http://en.wikipedia.org/wiki/Art_gallery_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-150http://en.wikipedia.org/w/index.php?title=Planar_partitioning&action=edit&redlink=1http://en.wikipedia.org/wiki/Motion_planninghttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-149http://en.wikipedia.org/wiki/Unit_disk_graphhttp://en.wikipedia.org/wiki/Euclidean_minimum_spanning_treehttp://en.wikipedia.org/wiki/Tree_(graph_theory)


13/17

Decoding of linear codes

ShapleyShubik power index

Clustering problem

Randomization test for matched pairs

Maximum likelihood ranking

Matrix domination

Matrix cover

Simply deviated disjunctionDecision tree

Minimum weight and/or graph solution

Fault detection in logic circuits

Fault detection in directed graphs

Fault detection with test points

Three-dimensional Ising model[151]

Circuit satisfiability problem

See also

Karp's 21 NP-complete problems

List of PSPACE-complete problems

Notes

1. ^ abcdefghijklmnopqrstu Karp (1972)

2. ^ Garey & Johnson (1979): GT13. ^ Garey & Johnson (1979): GT2

4. ^ Garey & Johnson (1979): GT3








12. ^ Minimum Independent Dominating Set (http://www.csc.kth.se/~viggo/wwwcompendium/node14.html)









21. ^ ab Garey & Johnson (1979): GT56

22. ^ ab Arnborg, Corneil & Proskurowski (1987)





http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-28http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-27http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-26http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-25http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-24http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-23http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFArnborgCorneilProskurowski1987http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-acp1987_22-1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-acp1987_22-0http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-.7B.7Bharvtxt.7CGarey.7CJohnson.7C1979.7D.7D:_GT56_21-1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-.7B.7Bharvtxt.7CGarey.7CJohnson.7C1979.7D.7D:_GT56_21-0http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-20http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-19http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-18http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-17http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-16http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-15http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-14http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-13http://www.csc.kth.se/~viggo/wwwcompendium/node14.htmlhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-12http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-11http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-10http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-9http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-8http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-7http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-6http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-5http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-4http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-3http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFGareyJohnson1979http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-2http://en.wikipedia.org/wiki/List_of_NP-complete_problems#CITEREFKarp1972http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-20http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-19http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-18http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-17http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-16http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-15http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-14http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-13http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-12http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-11http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-10http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-9http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-8http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-7http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-6http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-5http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-4http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-3http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-2http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-1http://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_ref-karp_1-0http://en.wikipedia.org/wiki/List_of_PSPACE-complete_problemshttp://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problemshttp://en.wikipedia.org/wiki/Circuit_satisfiability_problemhttp://en.wikipedia.org/wiki/List_of_NP-complete_problems#cite_note-151http://en.wikipedia.org/wiki/Ising_modelhttp://en.wikipedia.org/wiki/Test_pointhttp://en.wikipedia.org/wiki/Fault_detectionhttp://en.wikipedia.org/wiki/Directed_graphhttp://en.wikipedia.org/wiki/Fault_detectionhttp://en.wikipedia.org/wiki/Logic_circuithttp://en.wikipedia.org/wiki/Fault_detectionhttp://en.wikipedia.org/w/index.php?title=Minimum_weight_and/or_graph&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Decision_tree_problem&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Simply_deviated_disjunction&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Matrix_cover&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Matrix_domination&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Maximum_likelihood_ranking&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Matched_pair&action=edit&redlink=1http://en.wikipedia.org/wiki/Randomization_testhttp://en.wikipedia.org/w/index.php?title=Clustering_problem&action=edit&redlink=1http://en.wikipedia.org/wiki/Shapley%E2%80%93Shubik_power_indexhttp://en.wikipedia.org/wiki/Linear_code


14/17





















50. ^ Kashiwabara & Fujisawa (1979); Ohtsuki et al. (1979); Lengauer (1981).

















67. ^ Garey & Johnson (1979): GT6568. ^ "Normalized Cuts and Image Segmentation" (http://www.cs.berkeley.edu/~malik/papers/SM-ncut.pdf) .

IEEE. 20 October 2009. http://www.cs.berkeley.edu/~malik/papers/SM-ncut.pdf.

69. ^ ab "On the computational complexity of upward and rectilinear planarity testing". Lecture Notes in Computer

Science. 894/1995. 1995. pp. 286297. doi:10.1007/3-540-58950-3_384 (http://dx.doi.org/10.1007%2F3-540-

58950-3_384) .

70. ^ Garey & Johnson (1979): SP1




74. ^ Garey & Johnson (1979): SP575. ^ Garey & Johnson (1979): SP6




^
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81. ^ Garey & Johnson (1979): SR1






87. ^ Garey & Johnson (1979): SR788. ^ Garey & Johnson (1979): SR8




















108. ^ Garey & Johnson (1979): SR28109. ^ Garey & Johnson (1979): SR29








117. ^ http://www.cs.rpi.edu/~civria/max-vol-inapprox.pdf

118. ^ Yato, Takauki (2003). "Complexity and Completeness of Finding Another Solution and its Application toPuzzles". CiteSeerX: 10.1.1.103.8380 (http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.8380) .

119. ^ R. Clifford, M. Jalsenius, A. Montanaro and B. Sach (2010-08-19). The Complexity of Flood Filling Games.

arXiv:1001.4420 (http://arxiv.org/abs/1001.4420) .

120. ^ Malte Helmert, Complexity results for standard benchmark domains in planning, Artificial Intelligence Journal

143(2):219-262, 2003.

121. ^ Holzer & Ruepp (2007)

122. ^ Klker, Jonas (2012). Kurodoko is NP-complete

(https://www.jstage.jst.go.jp/article/ipsjjip/20/3/20_694/_article) .

https://www.jstage.jst.go.jp/article/ipsjjip/20/3/20_694/_article.

123. ^ Cormode, Graham (2004). "The hardness of the lemmings game, or Oh no, more NP-completeness proofs"

(http://dimacs.rutgers.edu/~graham/pubs/papers/cormodelemmings.pdf) .http://dimacs.rutgers.edu/~graham/pubs/papers/cormodelemmings.pdf.

124. ^ Klker, Jonas (2012). The Magnets puzzle is NP-Complete

(https://www.jstage.jst.go.jp/article/ipsjjip/20/3/20_707/_article) .

https://www.jstage.jst.go.jp/article/ipsjjip/20/3/20_707/_article.

^ " "
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