gerth stølting brodal 1 closing a classical data structure problem gerth stølting brodal : strict...
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Gerth stølting Brodal
1
Closing a Classical Data Structure Problem
Gerth Stølting Brodal
:
Strict Fibonacci Heaps
joint work with
George Lagogiannis Robert Endre Tarjan Athens Princeton & HP
44th Annual ACM Symposium on Theory of Computing, May 2012
Gerth stølting Brodal
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(J,6)
The Problem
(A,27)
(C,11)(M,36) (B,14)
(X,86) INSERT(value, key) FINDMIN DELETE / DELETEMIN MELD(Q1,Q2) DECREASEKEY(value, Δ)
(K,54)
(D,24)(Z,29)(W,6)
Q1
Q2
12
A 15
15
1
812
9
1625
11 3
1322
115
14
10
6217 4
19
Applications t
s Shortest Path Problem Dijkstra (1956)
Minimum Spanning Tree Borůvka (1926)
Jarník (1930)
(n node, m edges)
15
1
812
9
1625
11 3
1322
115
14
10
6217 4
19
(m+n)∙log n
m+n∙log n
m∙β(m,n)
MST only
INSERT/DELETEMIN
+ DECREASEKEY
+ DECREASEKEY
Fredman, Tarjan 1984
Fredman, Tarjan 1984
Priority queue
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Williams1964
Vuillemin1978
FredmanTarjan1984
Tarjanet al.1988
Brodal1995
Brodal1996
BrodalLagogianis
Tarjan2012
Insert log n log n 1 1 1 1 1 1 1
FindMin 1 1 1 1 1 1 1 1 1
Delete log n log n log n n log n log n log n log n log n
Meld - log n 1 1 1 log n 1 1 1
DecreaseKey log n log n log n n 1 1 log n 1 1
History
Amortized complexity (Tarjan 1983)CONFERENCE REVIEWS
This paper closes one of the few open problems in the area of comparison-based priority queues
Other PQs from the 1990s ... were extremely complicated The data structure is genuinely simple
Binary heaps
Binomial queues
Fibonacc
i heaps
Run-relaxed heaps
Arrays Complicated
Strict
Fibonacc
i
h
eaps
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Binary heaps1964
Binomial queues
1978
Fibonacciheaps1984
Run-relaxed heaps1988
Brodal1995
Brodal1996
Strict Fibonacci heaps2012
Heap-order
Rigid structure
Forest
Linking
Subtrees cut
Cascades Amortized
DECREASEKEY
Global control
Redundant counters
Local control
Redundant counters
Local redundant counters
Heap order violations
Global partial control
Pigenhole principle
Technical History
36
27
13
54
86
6
Binary heaps
7
16
42
1117
86
64
Min
8 243
Bionomial queuesFibonacci heaps
single tree
27
12
34
Gerth stølting Brodal
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Thank You
don’t give up Peter Gabriel (1985)
((( I worked on the heap problem 1994-2012 )))