An Interactive Tutorial for

NP-Completeness

MASTERS THESIS

BY

NABANITA MAJI

ADVISOR - DR. CLIFFORD SHAFFER

MAY - 2015

Outline

Background and MotivationVisualizations

The NP-Complete Problems

Practice Exercises on NP-Complete Problem Instances.

Proof of NP-Completeness

Analysis of UsageConclusion and Future work

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NP-Completeness

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Students’ perception of NP-Completeness

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2%

20%

64%

14%

Not at all difficult.

Somewhat less difficult

Average difficulty

Somewhat more difficult

Much more difficult

Related Work

“Using Interactive Visualization for Teaching the Theory of NP- completeness.”

“Incorporating an interactive visualization of NP-Completeness proofs into a web-based learning environment.”

“Visualizing NP-completeness through circuit-based widgets.”

GraphBench

AlViE

Swan

5/19/2015

Tools and Framework

OpenDSA

JSAV - JavaScript Algorithm Visualization library

Khan Academy exercises

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Outline

Background and MotivationVisualizations

The NP-Complete Problems

Practice Exercises on NP-Complete Problem Instances.

Proof of NP-Completeness

Analysis of UsageConclusion and Future work

5/19/2015

NP-Complete problems covered:

Circuit-SAT

SAT

3-SAT

Clique

Independent Set

Vertex Cover

Hamiltonian Cycle

Traveling Salesman.

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Outline

Background and MotivationVisualizations

The NP-Complete Problems

Practice Exercises on NP-Complete Problem Instances.

Proof of NP-Completeness

Analysis of UsageConclusion and Future work

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Introducing the problem

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Explanation of relevant context (Example)

Definition of the problem

Illustration with examples.

The NP-Complete problems

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Circuit Satisfiability problem (Circuit-SAT)The Formula Satisfiability problem (SAT)The 3CNF Satisfiability problem ( 3SAT )The Clique problemThe Independent Set problemThe Vertex Cover problemThe Hamiltonian Cycle problemThe Traveling Salesman problem

Outline

Background and MotivationVisualizations

The NP-Complete Problems

Practice Exercises on NP-Complete Problem Instances.

Proof of NP-Completeness

Analysis of UsageConclusion and Future work

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Practice Exercises – Why?

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Better illustration of the problem

Hands-on experience on problem instances

Help to appreciate the computation complexity.

Practice Exercises – Design aspects

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Generation of problem instances

Level of Difficulty

Solution and Verification

The Practice Exercises

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3-SATThe Maximum Clique problem The Maximum Independent Set problemThe Minimum Vertex Cover problemThe Hamiltonian cycle problemThe Traveling Salesman problem

Outline

Background and MotivationVisualizations

The NP-Complete Problems

Practice Exercises on NP-Complete Problem Instances.

Proof of NP-Completeness

Analysis of UsageConclusion and Future work

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Proving NP-Completeness

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NP NP-HardNP-Complete

Reductions

Reductions

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Proof of NP-Completeness

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The visualizations should include –

Description of each step of a reduction.

Explanation of correctness of the reduction.

Illustration using examples.

Order of Reductions

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Reductions in proving NP-Completeness

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Reduction of Circuit-SAT to SATReduction of SAT to 3-SATReduction of 3-SAT to Clique problemReduction of Clique to Independent Set problemReduction of Independent Set to Vertex Cover problemReduction of 3-SAT to Hamiltonian Cycle problemReduction of Hamiltonian Cycle to Traveling Salesman problem

Outline

Background and MotivationVisualizations

The NP-Complete Problems

Practice Exercises on NP-Complete Problem Instances.

Proof of NP-Completeness

Analysis of UsageConclusion and Future work

5/19/2015

Hypothesis

Students would spend a reasonable amount of time on the tutorial if it helps in their learning.

Students would have a good experience with the tutorial.

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Analysis of Usage – Methodology

The tutorial was introduced as a supplementary resource in CS 5114 and CS 4104 in Spring 2015.

Interaction logs : We analyzed the logs of students’ interactions with the tutorial.

Student survey : We collect feedback from students in the form of a survey.

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Challenges in analyzing Interaction logs

Distinguishing between users.

Distinguishing between actual usage and idle time.

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CS-5114 : Categorized Usage

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CS 5114 : Categorized usage

Theory Reduction Intro Proof

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CS 5114 Analysis of time spent per module

LimComp Reduction NPComplete hamiltonianCycle

circuitSAT NPCoping provingNPC threeSAT

SAT circuitSAT_to_SAT SAT_to_threeSAT clique

independentSet vertexCover TSP threeSAT_to_clique

clique_to_independentSet independentSet_to_vertexCover threeSAT_to_hamiltonianCycle hamiltonianCycle_to_TSP

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CS-4104 : Categorized Usage

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4104 Categorized usage analysis

Theory Reduction Intro Proof

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CS-4104 : Usage per module

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CS 4104 Analysis of time spent per module

LimComp Reduction NPComplete circuitSAT circuitSAT_to_SAT

threeSAT clique provingNPC threeSAT_to_hamiltonianCycle independentSet

SAT TSP vertexCover hamiltonianCycle SAT_to_threeSAT

threeSAT_to_clique NPCoping independentSet_to_vertexCover clique_to_independentSet hamiltonianCycle_to_TSP

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Time spent of exercises

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Analysis of Exercises

hamiltonianCycle_KA threeSAT_KA clique_KAindependentSet_KA vertexCover_KA TSP_KA

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Overall usage for CS 5114

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CS 5114 Analysis of time spent per module

LimComp Reduction NPComplete hamiltonianCyclecircuitSAT NPCoping provingNPC threeSATSAT circuitSAT_to_SAT SAT_to_threeSAT cliqueindependentSet vertexCover TSP threeSAT_to_cliqueclique_to_independentSet independentSet_to_vertexCover threeSAT_to_hamiltonianCycle hamiltonianCycle_to_TSP

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CS 4104 Analysis of time spent per module for finals

LimComp Reduction NPComplete circuitSAT circuitSAT_to_SAT

threeSAT clique provingNPC threeSAT_to_hamiltonianCycle independentSet

SAT TSP vertexCover hamiltonianCycle SAT_to_threeSAT

threeSAT_to_clique NPCoping independentSet_to_vertexCover clique_to_independentSet hamiltonianCycle_to_TSP

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Student Survey

CS 5114

• 23 out of 34 responded to the survey

• Average time spent as reported - 2.28 hours

• 65% found it useful for their homework

• 82% say they will use the tutorial to prepare for finals.

• 97% of the students provided a positive feedback when asked about their experience with the tutorial.

CS 4104

• 36 out of 62 responded to the survey

• Average time spent as reported - 32 minutes

• 19% found it useful for their homework

• 86% say the tutorial will be helpful for their finals.

• 72% of the students had a positive feedback when asked about their experience with the tutorial.

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Outline

Background and MotivationVisualizations

The NP-Complete Problems

Practice Exercises on NP-Complete Problem Instances.

Proof of NP-Completeness

Analysis of UsageConclusion and Future work

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Conclusion

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18 visualizations and 6 practice exercises in the tutorial.

Students think it is a good resource.

They use it on a need-to-know basis.

Future work

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Visualizations on more NP-Complete problems.

Pedagogical evaluation of the material.

Thank you

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Special mentions:

Dr . Cliff Shaffer

Dr. Lenwood Heath

Mohammed Farghally

Questions ??