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A Goal-Directed Shortest Path Algorithm Using Precomputed Cluster Distances


Maue,  Jens
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Maue, J. (2006). A Goal-Directed Shortest Path Algorithm Using Precomputed Cluster Distances. Master Thesis, Universität des Saarlandes, Saarbrücken.

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This thesis introduces a new acceleration heuristic for shortest path queries, called the PCD algorithm (\textbf{P}recomputed \textbf{C}luster \textbf{D}istances). PCD precomputes shortest path distances between the partitions of the input graph, which can be obtained by any graph partitioning method. Since the number of partitions can be varied between one and the number of nodes, the method presents an interpolation between all pairs and ordinary single source single target shortest path search. This allows a flexible trade-off between preprocessing time and space on the one hand and query time on the other, allowing significant speedups even for a sublinear amount of extra space. The method can be applied to arbitrary graphs with non-negative edge weights and does not afford a layout. Experiments on large street networks with a suitable clustering method are shown to yield average speedups of up to 114.9 for PCD as a stand-alone method. Furthermore, the algorithm's space-efficiency, simplicity, and goal-directed behaviour make PCD an alternative method to provide other acceleration heuristics with goal-direction.