Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Buckets, heaps, lists, and monotone priority queues
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Bidirectional Heuristic Search Again
Journal of the ACM (JACM)
Algorithm 360: shortest-path forest with topological ordering [H]
Communications of the ACM
Computing the nxm shortest path efficiently
Journal of Experimental Algorithmics (JEA)
Priority Queues: Small, Monotone and Trans-dichotomous
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Shortest Path Algorithms: An Evaluation Using Real Road Networks
Transportation Science
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Highway hierarchies hasten exact shortest path queries
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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The best known algorithm for the one-to-all shortest path problem is Dijkstra's algorithm, which can achieve time complexity O(|E| + |V|log(|V|)) by the implementation of data structures like buckets. While for one-to-some shortest path problem, no matter how small the "some" is, the time complexity of Dijkstra's algorithm remains O(|E| + |V|log(|V|)) and it often still needs to explore a large part of the graph and thus is not efficient. This paper proposes a novel algorithm which computes the shortest paths bidirectionally with A*algorithm multiple times to solve the one-to-some shortest path problem on road maps efficiently, where the size of the destination set is much smaller than the total number of vertices in the graph. The experiments on both randomly generated graphs and real road maps show that our algorithm is more space and time efficient than Dijkstra's algorithm with buckets, one of the most efficient algorithm for one-to-some shortest path problem.