@MISC{Raman96fastalgorithms, author = {Rajeev Raman}, title = {Fast Algorithms for Shortest Paths and Sorting}, year = {1996} }

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Abstract

A priority queue (pq) is said to be monotone if the value of the smallest element stored in the priority queue is a non-decreasing function of time. We consider the problem of maintaining a monotone priority queue on a set of integers in the range 0 : : 2 w \Gamma 1 on a unit-cost RAM with word size w bits. We give a monotone pq that, starting with an empty collection of items, processes a sequence of n insert and delete-mins and m decrease-keys in O(m+ n p log n log log n) time. As a consequence, the single-source shortest paths problem on graphs with n nodes and m edges and integer edge costs in the range 0 : : 2 w \Gamma 1 can be solved in O(m+n p log n log log n) time, and n integers each in the range 0 : : 2 w \Gamma 1 can be sorted in O(n p log n log log n) time. All the above results use only unit-time RAM instructions from the class ac 0 and require linear space. 1 Introduction Priority queues (pqs) are among the most fundamental of data structures, and have been...