We propose a simple and effective heuristic that allows fast generation of a large set of shortest path alternatives in weighted directed graphs. The heuristic is based on existing deviation path algorithms for exact k shortest paths. It precalculates a backward shortest path tree and thus avoids doing many shortest path computations, but as a result it does not necessarily find the exact set of k shortest paths.
Computational results on real-world road networks are reported. Our tests show that the quality of the paths produced by the heuristic is most satisfactory: typically, the kth path found by the heuristic is less than 1% longer than the exact kth shortest path, for values of k up to 10,000. Moreover, the heuristic runs very fast.
We also show how the heuristic can be enhanced to an exact k shortest paths algorithm, which performs well in comparison with the existing exact k shortest path algorithms
This paper describes ongoing PhD research on applications of graph algorithms in Geographical Information Systems. Many GIS problems can be translated into a graph problem, especially in the domain of routing in road networks. Our research aims to evaluate and develop efficient methods for different variants of the routing problem. Standard existing shortest path algorithms are not always suited for use in road networks, e.g. in a realistic situation forbidden turns and turn penalties need to be taken into account. An experimental evaluation of different methods for this purpose is presented. Another interesting problem is the generation of alternative routes. This can be modelled as a k shortest paths problem, where a ranking of k paths is desired rather than only the shortest path itself. A new heuristic approach for generating alternative routes is presented and evaluated.
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