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Multicuts in Unweighted Graphs with Bounded Degree and Bounded Tree-Width

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Integer Programming and Combinatorial Optimization (IPCO 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1412))

Abstract

The Multicut problem is defined as follows: given a graph G and a collection of pairs of distinct vertices (s i; t i) of G, find a small- est set of edges of G whose removal disconnects each s i from the corre- sponding t i. Our main result is a polynomial-time approximation scheme for Multicut in unweighted graphs with bounded degree and bounded tree-width: for any ∈ > 0, we presented a polynomial-time algorithm with performance ratio at most 1 + ∈. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provided some hardness results. We proved that Multicut is still NP-hard for binary trees and that, unless P = NP, no polynomial-time approximation scheme exists if we drop any of the the three conditions: unweighted, bounded-degree, bounded-tree-width. Some of these results extend to the vertex version of Multicut.

Research supported in part by NSF grant CCR-9319106.

Research partially supported by NSF grant CCR-9319106 and by FAPESP (Proc. 96/04505-2).

Research supported in part by ProNEx (MCT/FINEP) (Proj. 107/97) and FAPESP (Proc. 96/12111-4).

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Author information

Authors and Affiliations

  1. College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332-0280, USA

    Gruia Călinescu

  2. Department of Computer Science, University of São Paulo, Rua do Matao, 1010, 05508-900, Sao Paulo, Brazil

    Cristina G. Fernandes

  3. CNRS, Paris, France

    Bruce Reed

  4. Department of Computer Science, University of São Paulo, Brazil

    Bruce Reed

Authors
  1. Gruia Călinescu
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  2. Cristina G. Fernandes
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  3. Bruce Reed
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Editor information

Editors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University, 6020 Annapolis, Houston, TX, 77005, USA

    Robert E. Bixby

  2. PROS Strategic Solutions, 3223 Smith Street, Houston, TX, 77006, USA

    E. Andrew Boyd

  3. Department of Industrial, Engineering, Texas A&M University, 1000 Country Place Dr. Apt. 69, Houston, TX, 77079, USA

    Roger Z. Ríos-Mercado

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© 1998 Springer-Verlag Berlin Heidelberg

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Călinescu, G., Fernandes, C.G., Reed, B. (1998). Multicuts in Unweighted Graphs with Bounded Degree and Bounded Tree-Width. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_11

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  • DOI: https://doi.org/10.1007/3-540-69346-7_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64590-0

  • Online ISBN: 978-3-540-69346-8

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