Skip to main content
SpringerLink
Log in

An extension of the könig-egerváry property to node-weighted bidirected graphs

  • Published:
Mathematical Programming Submit manuscript

Abstract

Given a bidirected graphG and a vectorb of positive integral node-weights, an integer linear program IP is defined on (G, b). IP generalizes the node packing problem on a node-weighted (undirected) graph in the sense that it reduces to the latter whenG is undirected. A polynomial time algorithm is given that recognizes whether CP (the linear program obtained by relaxing the integrality constraints of IP) has an integral optimal solution. Also an efficient method for solving the linear programming dual of CP is described.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Aspvall, M.F. Plass and R.E. Tarjan, “A linear-time algorithm for testing the truth of certain quantitative Boolean formulas,”Information Processing Letters 8 (1979) 121–123.

    Google Scholar 

  2. J.-M. Bourjolly, “Integral and fractional node-packing, and pseudo-Boolean programming,” Ph.D. Thesis, University of Waterloo, 1986.

  3. J.-M. Bourjolly, P.L. Hammer and B. Simeone, “Node-weighted graphs having the König-Egerváry property,”Mathematical Programming Study 22 (1984) 44–63.

    Google Scholar 

  4. J. Edmonds and E.L. Johnson, “Matching: A well-solved class of integer linear programs,” in: R. Guy et al., eds.,Combinatorial Structures and their Applciations (Gordon and Breach, New York, 1970; Proceedings of the Calgary Symposium, June 1969).

    Google Scholar 

  5. J. Edmonds and R.M. Karp, “Theoretical improvements in algorithmic efficiency for network flow problems,”Journal of the Association for Computing Machinery 19 (1972) 248–264.

    Google Scholar 

  6. J. Green-Krótki, “Matching polyhedra,” M.Sc. Thesis, Carleton University, 1980.

  7. P.L. Hammer, P. Hansen and B. Simeone, “Roof duality, complementation and persistency in quadratic 0–1 optimization,”Mathematical Programming 28 (1984) 121–155.

    Google Scholar 

  8. Y. Ikura and G.L. Nemhauser, “An efficient primal simplex algorithm for maximum weighted vertex packing on bipartite graphs,”Annals of Discrete Mathematics 16 (1982) 149–168.

    Google Scholar 

  9. J.L. Kennington and R.V. Helgason,Algorithms for Network Programming (Wiley, 1980).

  10. A.B. Marsh, III, “Matching algorithms,” Ph.D. Thesis, The Johns Hopkins University, 1979.

Download references

Author information

Authors and Affiliations

  1. Department of Decision Sciences & Management Information Systems, Concordia University, Montreal, Quebec, Canada

    Jean-Marie Bourjolly

Authors
  1. Jean-Marie Bourjolly
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Natural Sciences and Engineering Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bourjolly, JM. An extension of the könig-egerváry property to node-weighted bidirected graphs. Mathematical Programming 41, 375–384 (1988). https://doi.org/10.1007/BF01580775

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01580775

Key words

Search

Navigation