Fibonacci Heaps and Their Uses in Improved Network optimization algorithms

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Fibonacci Heaps and Their Uses in Improved Network optimization algorithms (1987)

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by Michael L. Fredman , Robert Endre Tarjan

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739 - 18 self

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@MISC{Fredman87fibonacciheaps,
    author = {Michael L. Fredman and Robert Endre Tarjan},
    title = {Fibonacci Heaps and Their Uses in Improved Network optimization algorithms},
    year = {1987}
}

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Abstract

In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in qlogn) amortized time and all other standard heap operations in o ( 1) amortized time. Using F-heaps we are able to obtain improved running times for several network optimization algorithms. In particular, we obtain the following worst-case bounds, where n is the number of vertices and m the number of edges in the problem graph: ( 1) O(n log n + m) for the single-source shortest path problem with nonnegative edge lengths, improved from O(m logfmh+2)n); (2) O(n*log n + nm) for the all-pairs shortest path problem, improved from O(nm lo&,,,+2,n); (3) O(n*logn + nm) for the assignment problem (weighted bipartite matching), improved from O(nm log0dn+2)n); (4) O(mj3(m, n)) for the minimum spanning tree problem, improved from O(mloglo&,,.+2,n), where j3(m, n) = min {i 1 log % 5 m/n). Note that B(m, n) 5 log*n if m 2 n. Of these results, the improved bound for minimum spanning trees is the most striking, although all the

Keyphrases

fibonacci heap all-pairs shortest path problem minimum spanning tree problem priority queue binomial queue assignment problem new data structure improved running time n-item heap standard heap operation problem graph nm lo minimum spanning tree nonnegative edge length following worst-case bound logn nm f-heaps support arbitrary deletion single-source shortest path problem several network optimization algorithm weighted bipartite matching

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