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PTAS for Densest k-Subgraph in Interval Graphs

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Algorithms and Data Structures (WADS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6844))

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Abstract

Given an interval graph and integer k, we consider the problem of finding a subgraph of size k with a maximum number of induced edges, called densest k-subgraph problem in interval graphs. It has been shown that this problem is NP-hard even for chordal graphs [17], and there is probably no PTAS for general graphs [12]. However, the exact complexity status for interval graphs is a long-standing open problem [17], and the best known approximation result is a 3-approximation algorithm [16]. We shed light on the approximation complexity of finding a densest k-subgraph in interval graphs by presenting a polynomial-time approximation scheme (PTAS), that is, we show that there is an (1+ε)-approximation algorithm for any ε > 0, which is the first such approximation scheme for the densest k-subgraph problem in an important graph class without any further restrictions.

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Authors and Affiliations

  1. IBM Research, Zurich, Switzerland

    Tim Nonner

Authors
  1. Tim Nonner
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, 11201, New York, NY, USA

    John Iacono

  3. School of Computer Science, Herzberg Laboratories, Carleton University, Herzberg Building, Room 5350, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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Nonner, T. (2011). PTAS for Densest k-Subgraph in Interval Graphs. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_53

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  • DOI: https://doi.org/10.1007/978-3-642-22300-6_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22299-3

  • Online ISBN: 978-3-642-22300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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