Faster algorithms for the shortest path problem

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

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