Browse > Article

A Study on a new Algorithm for K Shortest Paths Problem  

Chang, Byung-Man (서울산업대학교 산업정보시스템공학과)
Publication Information
Korean Management Science Review / v.25, no.2, 2008 , pp. 81-88 More about this Journal
Abstract
This paper presents a new algorithm for the K shortest paths problem in a network. After a shortest path is produced with Dijkstra algorithm. detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set. this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated until the $K^{th}-1$ path of the set is obtained. The computational results for networks with about 1,000,000 nodes and 2,700,000 arcs show that this algorithm can be applied to a problem of generating the detouring paths in the metropolitan traffic networks.
Keywords
K Shortest Paths; Detour Paths; Dijkstra Method;
Citations & Related Records
연도 인용수 순위
  • Reference
1 장병만, 민윤홍, "복수최단경로 새로운 해법 연구", IE/MS 춘계공동학술대회 발표집(2008)
2 Dreyfus, S., "An appraisal of some shortest path algorithms," Oper Res, Vol.17, No.2 (1969), pp.395-412   DOI   ScienceOn
3 Hadjiconstantinou, E. and N. Christofides, "An efficient implementation of an algorithm for finding K shortest paths," Networks, Vol.34(1999), pp.88-101   DOI   ScienceOn
4 Katoh, N., T. Ibaraki, and H. Mine, "An efficient algorithm for K shortest simple paths," Networks, Vol.12(1982), pp.411-427   DOI   ScienceOn
5 Lawler, E., Combinatorial Optimization： Networks and Matroids, Holt Reinhart and Winston, New York, (1976), pp.100-104
6 Martins, E.Q., M. Pascoal, and J.L. Santos, "A new improvement for a K shortest paths algorithm," Investigacao Operacional, Vol. 21, No.1(2001), pp.47-60
7 Lawler, E., "A procedure for computing the K best solutions to discrete optimization problems and its application to the shortest path problem," Management Sci., Vol.18 (1972), pp.401-405   DOI   ScienceOn
8 Yen, J., "Finding the K shortest loopless paths in a network," Management Sci., Vol. 17(1971), pp.712-716   DOI   ScienceOn
9 Shier, D., "On algorithm for finding the K shortest paths in a network," Networks, Vol.9(1979), pp.195-214   DOI   ScienceOn
10 Dijkstra, E.W., "A note on two problems in connection with graphs," Numerische Mathematik, Vol.1(1959), pp.269-271   DOI
11 Eppstein, D., "Finding the K shortest paths," SIAM J.Comput., Vol.28, No.2(1998), pp. 652-673   DOI   ScienceOn
12 장병만, 김시곤, "유방향의 복수최단경로 해법 에 관한 연구", 한국SCM학회지, 제8권, 제1 호(2008), pp.83-92