Faster algorithms for the shortest path problem

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 + n a @@@@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].