1. 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

2. Gerth stølting Brodal 2 (J,6) The Problem (A,27) (C,11) (M,36) (B,14) (X,86)  I NSERT (value, key)  F IND M IN  D ELETE / D ELETE M IN  M ELD (Q 1,Q 2 )  D ECREASE K EY (value, Δ) (K,54) (D,24) (Z,29)(W,6) Q1Q1 Q2Q2 12 A 15 15 1 8 12 9 16 25 11 3 13 22 11 5 14 10 6 2 17 4 19 Applications t s  Shortest Path Problem  Dijkstra (1956)  Minimum Spanning Tree  Borůvka (1926) Jarník (1930) (n node, m edges) 15 1 8 12 9 16 25 11 3 13 22 11 5 14 10 6 2 17 4 19 (m+n)∙log n m+n∙log n m∙β(m,n) MST only I NSERT /D ELETE M IN + D ECREASE K EY Fredman, Tarjan 1984 Priority queue

3. Gerth stølting Brodal 3 Williams 1964 Vuillemin 1978 Fredman Tarjan 1984 Tarjan et al. 1988 Brodal 1995 Brodal 1996 Brodal Lagogianis Tarjan 2012 Insertlog n 1111111 FindMin111111111 Deletelog n n Meld-log n111 111 DecreaseKeylog n n11 11 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 Fibonacci heaps Run-relaxed heaps Arrays Complicated Strict Fibonacci heaps

4. Gerth stølting Brodal 4 Binary heaps 1964 Binomial queues 1978 Fibonacci heaps 1984 Run-relaxed heaps 1988 Brodal 1995 Brodal 1996 Strict Fibonacci heaps 2012 Heap-order Rigid structure Forest Linking Subtrees cut Cascades  Amortized D ECREASE K EY 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 11 17 86 6 4 Min 8 243 Bionomial queuesFibonacci heaps single tree 27 12 34

5. Gerth stølting Brodal 5 Thank You don’t give up  Peter Gabriel (1985) ( ( ( I worked on the heap problem 1994-2012 ) ) )