Abstract

. As an alternative to the Fibonacci heap, we design a new data structure called a 2-3 heap, which supports m decrease-key, and n insert operations and delete-min operations in O(m + n log n) time. The merit of the 2-3 heap is that it is conceptually simpler and easier to implement. The new data structure will have a wide application in graph algorithms. 1 Introduction Since Fredman and Tarjan [7] published Fibonacci heaps in 1987, there has not been an easy alternative that can support n insert and delete-min operations, and m decrease-key operations in O(m+n log n) time. The relaxed heaps by Driscoll, et. al [6] have the same overall complexity with decrease-key in O(1) worst case time, but are di#cult to implement. Logarithm here is with base 2, unless otherwise specified. Two representative application areas for these operations will be the single source shortest path problem and the minimum cost spanning tree problem. Direct use of these operations in Dijkstra's [5] and Pri...

Citations

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