Skip to main content
Log in

Local and variable neighborhood search for the k-cardinality subgraph problem

Journal of Heuristics Aims and scope Submit manuscript

Abstract

The minimum weighted k-cardinality subgraph problem consists of finding a connected subgraph of a given graph with exactly k edges whose sum of weights is minimum. For this NP-hard combinatorial problem, only constructive types of heuristics have been suggested in the literature. In this paper we propose a new heuristic based on variable neighborhood search metaheuristic rules. This procedure uses a new local search developed by us. Extensive numerical results that include graphs with up to 5,000 vertices are reported. It appears that VNS outperforms all previous methods.

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

Access this article

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

  • Baum, B.E.: Toward practical ‘neural’ computation for combinatorial optimization problems. In: Deker, J. (ed.) Neural Networks for Computing. American Institute of Physics, New York (1986)

    Google Scholar 

  • Blum, C., Ehrgott, M.: Local search algorithms for the k-cardinality tree problem. Discrete Appl. Math. 128(2-3), 511–540 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Ehrgott, M.: Optimization problems in graphs under cardinality restrictions (in German). Master’s thesis, University of Kaiserslautern, Department of Mathematics (1992)

  • Ehrgott, M., Freitag, J.: K_TREE/K_SUBGRAPH: a program package for minimum weighted K-cardinality trees and subgraphs. Eur. J. Oper. Res. 93(1), 224–225 (1996)

    Article  MATH  Google Scholar 

  • Fischetti, M., Hamacher, H., Jörnsten, K., Maffioli, F.: Weighted k-cardinality trees: complexity and polyhedral structure. Networks 24, 11–21 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)

    Article  MATH  Google Scholar 

  • Hansen, P., Mladenović, N.: Variable neighborhood search. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics. Kluwer Academic, New York (2003)

    Google Scholar 

  • Jörnsten, K., Lokketangen, A.: Tabu search for weighted k-cardinality trees. Asia Pac. J. Oper. Res. 14(2), 9–26 (1997)

    MATH  Google Scholar 

  • Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24, 1097–1100 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Mladenović, N., Urošević, D.: Variable neighborhood search for the k-cardinality tree. In: Resende, M.G.C., de Sousa, J.P. (eds.) Metaheuristics: Computer Decision-Making. Kluwer Academic, Dordrecht (2003)

    Google Scholar 

  • Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36 (1957)

  • Urošević, D., Brimberg, J., Mladenović, N.: Variable neighborhood decomposition search for the edge weighted k-cardinality tree problem. Comput. Oper. Res. 31, 1205–1213 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nenad Mladenović.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brimberg, J., Mladenović, N. & Urošević, D. Local and variable neighborhood search for the k-cardinality subgraph problem. J Heuristics 14, 501–517 (2008). https://doi.org/10.1007/s10732-007-9046-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-007-9046-y

Keywords

Navigation