Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Representation of Edmonds' Algorithm for Finding Optimum Graph Branching on Associative Parallel Processors

  • Published:
Programming and Computer Software Aims and scope Submit manuscript

Abstract

In the paper, an efficient parallel implementation of Edmonds' algorithm is suggested for finding optimum graph branching on an abstract model of the SIMD type with vertical data processing (STAR machine). For this, associative parallel algorithms for finding critical circuit and its contraction, as well as for unfolding embedded critical circuits, are constructed for directed weighted graphs represented as a list of arcs and their weights. It is shown that the execution of Edmonds' algorithm on a STAR machine requires O(nlogn) time, where nis the number of graph vertexes. Basic advantages of the parallel implementation of Edmonds' algorithm compared to its implementation on sequential computers are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

REFERENCES

  1. Edmonds, J., Optimum Branchings, J. Res. Nat. Bur. Standards, 1967, no. 71B, pp. 233–240.

  2. Gabow, H.N., Galil, Z., Spencer, T., and Tarjan, R.E., Efficient Algorithms for Finding Minimum Spanning Trees in Undirected and Directed Graphs, Combinatorica, 1986, vol. 6, no. 2, pp. 109–122.

    Google Scholar 

  3. Gabow, H.N., Galil, Z., and Spencer, T., Efficient Implementation of Graph Algorithms Using Contraction, Proc. 25th Annual IEEE Symp. on Found. of Comp. Sci., 1984, pp. 347–357.

  4. Tarjan, R.E., Finding Optimum Branchings, Networks, 1977, no.7, pp. 25–35.

    Google Scholar 

  5. Camerini, R.M., Fratta, L., and Maffioli, F., A Note on Finding Optimum Branchigs, Networks, 1979, no. 9, pp. 309–312.

  6. Fet, Y.I., Vertical Processing Systems: A Survey, IEEE, Micro, 1995, pp. 65–75.

  7. Grosspietsch, K.E., Associative Processors and Memories: A Survey, IEEE, Micro, 1992, pp. 12–19.

  8. Nepomniaschaya, A.Sh. and Vladyko, M.A., Comparison of Models of Associative Computations, Programmirovanie, 1997, no. 6, pp. 41–50.

  9. Foster, C.C., Content Addressable Parallel Processors, New York: Van Nostrand Reinhold Co., 1976.

    Google Scholar 

  10. Gabow, H.N. and Tarjan, R.E., Efficient Algorihms for a Family of Matroid Intersection Problems,J. Algorithms, 1984, no. 5, pp 80–131.

  11. Karp, R.M., A Simple Derivation of Edmonds' Algorithm for Optimum Branchings, Networks, 1972, no.1, pp. 265–272.

    Google Scholar 

  12. Nepomniaschaya, A.S., An Associative Version of the Prim-Dijkstra Algorithm and Its Application to Some Graph Problems,Andrei Ershov Second Int. Memorial Conf. “Perspectives of System Informatics,” Lecture Notes in Computer Science, Berlin: Springer, 1996, vol. 1181, pp. 203–213.

    Google Scholar 

  13. Nepomniaschaya, A.S., Solution of Path Problems Using Associative Parallel Processors, Proc. of the Int. Conf. on Parallel and Distributed Systems, ICPADS'97, Seoul, Korea, IEEE Computer Society Press, 1997, pp. 610–617.

    Google Scholar 

  14. Minieka, E., Optimization Algorithms for Networks and Graphs, New York: Marcel Decker, 1978. Translated under the title Algoritmy optimizatsii na setyakh i grafakh, Moscow: Mir, 1981.

    Google Scholar 

  15. Nepomniaschaya, A.S., An Associative Algorithm for Finding Maximum-Weight Cycle in Directed Graphs, in Joint Bulletin of the Novosibirsk Computing Center and Ershov Institute of Informatics Systems, Computer Science Series, 1999, issue 11, pp. 45–58.

  16. Tarjan, R.E., Depth First Search and Linear Graph Algorithms, SIAM J. Comput, 1972, vol. 1, pp. 146–160.

    Google Scholar 

  17. Fredman, M.L. and Tarjan, R.E., Fibonacci Heaps and Their Uses in Improved Network Optimization Algorithms, J. ACM, 1987, vol. 34, no. 3, pp. 596–615.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nepomniaschaya, A.S. Representation of Edmonds' Algorithm for Finding Optimum Graph Branching on Associative Parallel Processors. Programming and Computer Software 27, 200–206 (2001). https://doi.org/10.1023/A:1010918704202

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010918704202

Keywords

Navigation