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Advances in Strict Fibonacci Heaps: Closing a Key Classical Data Structure Problem

This paper, a collaborative effort by Gerth Stølting Brodal, George Lagogiannis, and Robert Tarjan, addresses the longstanding open problem in the realm of comparison-based priority queues through the development of Strict Fibonacci Heaps. Presented at the 44th Annual ACM Symposium on Theory of Computing, the authors explore fundamental operations such as Insert, Delete, DecreaseKey, and their applications in Shortest Path and Minimum Spanning Tree problems. This novel data structure is simpler than previous efforts, promoting advancements in the efficient manipulation of priority queues.

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Advances in Strict Fibonacci Heaps: Closing a Key Classical Data Structure Problem

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  1. Closing a Classical Data Structure ProblemGerth Stølting Brodal : Strict Fibonacci Heaps joint work with George Lagogiannis Robert EndreTarjanAthensPrinceton & HP44th Annual ACM Symposium on Theory of Computing, May 2012

  2. The Problem (C,11) (M,36) (B,14) • Insert(value, key) • FindMin • Delete / DeleteMin • Meld(Q1,Q2) • DecreaseKey(value, Δ) (X,86) 12 • ShortestPathProblem • Dijkstra (1956) • Minimum SpanningTree • Borůvka (1926)Jarník (1930) (n node, m edges) Priorityqueue (A,27) (K,54) A 15 (W,6) (Z,29) t Applications (D,24) 3 3 11 11 • Insert/DeleteMin 4 4 17 17 6 6 • (m+n)∙log n • m+n∙logn • m∙β(m,n) 22 22 2 2 s 13 13 25 25 16 16 11 11 5 5 15 15 • Fredman, Tarjan 1984 10 10 1 1 14 14 19 19 9 9 8 8 • + DecreaseKey 12 12 • Fredman, Tarjan 1984 • MST • only • + DecreaseKey

  3. History StrictFibonacci heaps Run-relaxedheaps Binomial queues Fibonacciheaps Binaryheaps Arrays Complicated Amortizedcomplexity (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

  4. TechnicalHistory Min 7 4 13 12 11 16 17 27 86 27 34 24 42 54 36 86 • Binaryheaps • Bionomialqueues single tree

  5. ThankYou don’t give up Peter Gabriel (1985) ((( I workedon the heap problem 1994-2012 )))

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