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International Conference on Integer Programming and Combinatorial Optimization

IPCO 1995: Integer Programming and Combinatorial Optimization pp 29–39Cite as

Nonlinear formulations and improved randomized approximation algorithms for multicut problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 920))

Abstract

We introduce nonlinear formulations for the multiway cut and multicut problems. By simple linearizations of these formulations we derive several well known formulations and valid inequalities as well as several new ones. Through these formulations we establish a connection between the multiway cut and the maximum weighted independent set problem that leads to the study of the tightness of several LP formulations for the multiway cut problem through the theory of perfect graphs. We finally introduce a new randomized rounding heuristic to study the worst case bound of these formulations, obtaining a new bound of 2α(H)(1-1/k) for the multicut problem, where α(H) is the size of a maximum independent set in the demand graph H.

Research partially supported by a Presidential Young Investigator Award DDM-9158118 with matching funds from Draper Laboratory.

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Author information

Authors and Affiliations

  1. Sloan School of Management and Operations Research Center, MIT, 02139, Cambridge, MA

    Dimitris Bertsimas

  2. Operations Research Center, MIT, 02139, Cambridge, MA

    Chungpiaw Teo

  3. Fisher College of Business, Ohio State University, USA

    Rakesh Vohra

Authors
  1. Dimitris Bertsimas
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  2. Chungpiaw Teo
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  3. Rakesh Vohra
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Editor information

Egon Balas Jens Clausen

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© 1995 Springer-Verlag Berlin Heidelberg

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Bertsimas, D., Teo, C., Vohra, R. (1995). Nonlinear formulations and improved randomized approximation algorithms for multicut problems. In: Balas, E., Clausen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1995. Lecture Notes in Computer Science, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59408-6_39

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  • DOI: https://doi.org/10.1007/3-540-59408-6_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59408-6

  • Online ISBN: 978-3-540-49245-0

  • eBook Packages: Springer Book Archive

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