K⁎: A heuristic search algorithm for finding the k shortest paths

We present a directed search algorithm, called K^@?, for finding the k shortest paths between a designated pair of vertices in a given directed weighted graph. K^@? has two advantages compared to current k-shortest-paths algorithms. First, K^@? operates on-the-fly, which means that it does not require the graph to be explicitly available and stored in main memory. Portions of the graph will be generated as needed. Second, K^@? can be guided using heuristic functions. We prove the correctness of K^@? and determine its asymptotic worst-case complexity when using a consistent heuristic to be the same as the state of the art, O(m+nlogn+k), with respect to both runtime and space, where n is the number of vertices and m is the number of edges of the graph. We present an experimental evaluation of K^@? by applying it to route planning problems as well as counterexample generation for stochastic model checking. The experimental results illustrate that due to the use of heuristic, on-the-fly search K^@? can use less time and memory compared to the most efficient k-shortest-paths algorithms known so far.

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