Abstract
In this article, we present an implementation of a distributed branch and bound algorithm solving the Vertex Cover problem on a network of up to 63 Transputers.
We implemented two different strategies: The first parallelization of our branch and bound algorithm is fully distributed. Every processor performs the same algorithm but on a different part of the solution tree. In this case it is necessary to distribute subproblems among the processors to achieve a well balanced workload.
Our second strategy is based on a tree structured network, where all subproblems are stored at the root processor and the other processes work as slaves of this master process.
To show the performance of our strategies, we solved the Vertex Cover problem for graphs of up to 150 nodes and an average degree of 30. We were able to achieve a speedup of 57.35 for the first strategy on a 60 processor network and 62.11 for the second strategy on 63 processors, compared to a very efficient sequential algorithm.
This work was partly supported by the german research association (DFG)
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
E. Altmann, T. A. Marsland, T. Breitkreutz Accounting for Parallel Tree Search Overheads, Proceedings of the International Conference on Parallel Processing 1988, pp. 198–201
C. Beilken, F. Mattern, M. Reinfrank Verteilte Terminierung ein wesentlicher Aspekt der Kontrolle in verteilten Systemen Sonderforschungsbereich 124 ”VLSI Entwurfsmethoden und Parallelität”, Bericht Nr. 41/85, Dezember 1985
C. Berge The theory of graphs and its applications, Methuen, London 1962
A. Burns Programming in OCCAM 2, Addison Wesely 1988.
R. Feldmann, B. Monien, P. Mysliwietz, O. Vornberger Distributed Game Tree Search, to appear in: Kanal, Gopalakrishnan, Kumar, Parallel Algorithms for Machine Intelligence and Pattern Recognition, North Holland/ Elsevier Publ. Co.
M. R. Garey, D.S. Johnson Computers and Intractability: A Guide to the Theory of NP-Completeness, 1979 Freeman, San Francisco, Calif.
V. K. Janakiram, D. P. Agrawal, R. Mehrotra A randomized Parallel Branch and Bound Algorithm, Proceedings of the International Conference on Parallel Processing 1988, pp. 69–75
R. M. Karp, Y. Zhang, A randomized Parallel Branch and Bound Procedure, Proceedings of the ACM Symposium on Theory of Computing 1988, pp. 290–300
V. Kumar, V. Nageshwara Rao, K. Ramesh Parallel Depth First Search on the Ring Architecture International Conference on Parallel Processing, pp. 128–132
E. L. Lawler, D. E. Wood Branch and Bound Methods: A survey, Operations Research 14, 1966, pp. 699–719
F. C. H. Lin, R. M. Keller The Gradient Model Load Balancing Method, IEEE Transactions on Software Engineering, Vol. 13, No. 1 January 1987
B. Monien and O. Vornberger Parallel processing of combinatorial search trees, Processings International Workshop on Parallel Algorithms and Architectures, Math. Research Nr. 38, Akademie — Verlag Berlin, pp. 60–69, 1987
B. Monien, E. Speckenmeyer, O. Vornberger Upperbound for covering problems, Methods of operations research, 43, 1981, pp. 419–431
R. E. Tarjan, A. E. Trojanowski Finding a maximum independent set, SIAM J. Computing, Vol. 6, No. 3, September 1977, pp. 537–546
O. Vornberger and B. Monien Parallel alpha-beta versus parallel SSS*, Proceedings IFIP Conference on Distributed Processing, Distributed Processing, North Holland, pp. 613–625, 1987
O. Vornberger Implementing branch and bound in a ring of processors, Proceedings of CONPAR 86, Lecture Notes of Computer Science 237, Springer Verlag, pp. 157–164, 1986
O. Vornberger Load Balancing in a Network of Transputers, Distributed Algorithms 1987, Lecture Notes of Computer Science 312, Springer Verlag, pp. 116–126
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lüling, R., Monien, B. (1989). Two strategies for solving the vertex cover problem on a transputer network. In: Bermond, JC., Raynal, M. (eds) Distributed Algorithms. WDAG 1989. Lecture Notes in Computer Science, vol 392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51687-5_40
Download citation
DOI: https://doi.org/10.1007/3-540-51687-5_40
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51687-3
Online ISBN: 978-3-540-46750-2
eBook Packages: Springer Book Archive