Faster algorithms for the shortest path problem

  • Authors:
  • Ravindra K. Ahuja;Kurt Mehlhorn;James Orlin;Robert E. Tarjan

  • Affiliations:
  • Massachusetts Institute of Technology, Cambridge;Univ. des Saarlandes, Saarbru¨cken, W. Germany;Massachusetts Institute of Technology, Cambridge;Princeton Univ. Princeton, NJ

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1990

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Abstract

Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C, a one-level form of radix heap gives a time bound for Dijkstra's algorithm of O(m + n log C). A two-level form of radix heap gives a bound of O(m + n log C/log log C). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O(m + na @@@@log C). The best previously known bounds are O(m + n log n) using Fibonacci heaps alone and O(m log log C) using the priority queue structure of Van Emde Boas et al. [ 17].