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Packing and covering with linear programming: A survey

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  • Bentz, Cédric
  • Cornaz, Denis
  • Ries, Bernard

Abstract

This paper considers the polyhedral results and the min–max results on packing and covering problems of the decade. Since the strong perfect graph theorem (published in 2006), the main such results are available for the packing problem, however there are still important polyhedral questions that remain open. For the covering problem, the main questions are still open, although there has been important progress. We survey some of the main results with emphasis on those where linear programming and graph theory come together. They mainly concern the covering of cycles or dicycles in graphs or signed graphs, either with vertices or edges; this includes the multicut and integral multiflow problems.

Suggested Citation

  • Bentz, Cédric & Cornaz, Denis & Ries, Bernard, 2013. "Packing and covering with linear programming: A survey," European Journal of Operational Research, Elsevier, vol. 227(3), pages 409-422.
    • Handle: RePEc:eee:ejores:v:227:y:2013:i:3:p:409-422
    DOI: 10.1016/j.ejor.2012.11.045
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    Cited by:

    1. Subrata Mitra & Balram Avittathur, 2018. "Application of linear programming in optimizing the procurement and movement of coal for an Indian coal-fired power-generating company," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 45(3), pages 207-224, September.

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