Abstract
We develop parallel asynchronous implementations of some known and some new label-correcting methods for finding a shortest path from a single origin to all the other nodes of a directed graph. We compare these implementations on a shared-memory multiprocessor, the Alliant FX/80, using several types of randomly generated problems. Excellent (sometimes superlinear) speedup is achieved with some of the methods, and it is found that the asynchronous versions of these methods are substantially faster than their synchronous counterparts.
Similar content being viewed by others
References
Gallo, G., andPallottino, S.,Shortest Path Algorithms, Annals of Operations Research, Vol. 7, pp. 3–79, 1988.
Bertsekas, D. P.,An Auction Algorithm for the Shortest Path Problem, Mathematical Programming Study, Vol. 26, pp. 38–64, 1986.
Bertsekas, D. P., Pallottino, S., andScutella', M. G.,Polynomial Auction Algorithms for Shortest Paths, Computational Optimization and Applications, Vol. 4, pp. 99–125, 1995.
Helgason, R. V., andStewart, D.,One-to-One Shortest Path Problem: An Empirical Analysis with the Two-Tree Dijkstra Algorithm, Computational Optimization and Applications, Vol. 2, pp. 47–75, 1993.
Polymenakos, L., andBertsekas, D. P.,Parallel Shortest Path Auction Algorithms, Parallel Computing, Vol. 20, pp. 1221–1247, 1994.
Gallo, G., andPallottino, S.,Shortest Path Methods: A Unified Approach, Mathematical Programming Study, Vol. 26, pp. 38–64, 1986.
Bellman, R.,Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1957.
Bertsekas, D. P.,A Simple and Fast Label-Correcting Algorithm for Shortest Paths, Networks, Vol. 23, pp. 703–709, 1993.
Glover, F., Glover, R., andKlingman, D.,The Threshold Shortest Path Algorithm, Networks, Vol. 14, pp. 256–282, 1986.
Pape, U.,Implementation and Efficiency of Moore Algorithms for the Shortest Path Problem, Mathematical Programming, Vol. 7, pp. 212–222, 1974.
Bertsekas, D. P.,Linear Network Optimization: Algorithms and Codes, MIT Press, Cambridge, Massachusetts, 1991.
Bertsekas, D. P.,Distributed Dynamic Programming, IEEE Transactions on Automatic Control, Vol. 27, pp. 610–616, 1982.
Bertsekas, D. P., andGallager, R. G.,Data Networks, 2nd Edition, Prentice-Hall, Englewood Cliffs, New Jersey, 1992.
Bertsekas, D. P., andTsitsiklis, J. N.,Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
Mohr, T., andPasche, C.,Parallel Shortest Path Algorithm, Computing, Vol. 40, pp. 281–292, 1990.
Träff, J. L.,Precis: Distributed Shortest Path Algorithms, Proceedings of the 5th International PARLE Conference, Munich, Germany, 1993; Springer Verlag, Berlin, Germany, pp. 720–723, 1993.
Dung, T., Hao, J., andKokur, G.,Label-Correcting Shortest Path Algorithms: Analysis and Implementation, Unpublished Report, GTE Laboratories, Waltham, Massachusetts, 1993.
Bertsekas, D. P., andCastanon, D. A.,Parallel Asynchronous Implementations of the Auction Algorithm, Parallel Computing, Vol. 1, pp. 707–732, 1991.
Klingman, D., Napier, A., andStutz, J.,NETGEN: A Program for Generating Large-Scale (Un) Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems, Management Science, Vol. 20, pp. 814–822, 1974.
Bertsekas, D. P., Guerriero, F., andMusmanno, R.,Parallel Asynchronous Label-Correcting Methods for Shortest Paths, Report No. LIDS-P-2250, Massachusetts Institute of Technology, 1992.
Brown, A. A., andBartholomew-Biggs, M. C.,Some Effective Methods for Unconstrained Optimization Based on the Solution of Systems of Ordinary Differential Equations, Report No. 78, Numerical Optimisation Centre, Hatfield Polytechnic, Hatfield, England, 1987.
Author information
Authors and Affiliations
Additional information
Communicated by G. P. Papavassilopoulos
The authors acknowledge the director and the staff of CERFACS, Toulouse, France for the use of the Alliant FX/80.
This research was supported by the National Science Foundation under Grants 9108058-CCR, 9221293-INT, and 9300494-DMI.
Rights and permissions
About this article
Cite this article
Bertsekas, D.P., Guerriero, F. & Musmanno, R. Parallel asynchronous label-correcting methods for shortest paths. J Optim Theory Appl 88, 297–320 (1996). https://doi.org/10.1007/BF02192173
Issue Date:
DOI: https://doi.org/10.1007/BF02192173