The relaxed heap is a priority queue data structure that achieves the same amortized time bounds as the Fibonacci heap-a sequence of m decrease^key and n delete_min operations takes time 0{m + n log n). A variant of relaxed heaps achieves similar bounds in the worst case-0(1) time for decrease^key and O(log n) for delete.min. Relaxed heaps give a processor-efficient parallel implemetxtation of Dijkstra's shortest path algorithm, and hence other algorithms in network optimization. A relaxed heap is a type of binomial queue that allows heap order to be violated.
INTRODUCTIONThe Fihonacci heap data structure of Fredman and Tarjan allows an optimal implementation of Dijkstra's shortest path algorithm [3]. It is central to the hestknown algorithm for minimum spanning trees [5] and many other algorithms. These applications are based on the fact that, with a Fihonacci heap, a sequence of m decrease-key and n delete-min operations takes time 0[m + n log n). Equivalently, Fibonacci heaps achieve an amortized time of 0(1] for decrease-key and O[log n) for delete-min.
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