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International Workshop on Randomization and Approximation Techniques in Computer Science

International Workshop on Approximation Algorithms for Combinatorial Optimization

RANDOM 2001, APPROX 2001: Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques pp 147–158Cite as

The Maximum Acyclic Subgraph Problem and Degree-3 Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2129))

Abstract

We study the problem of finding a maximum acyclic subgraph of a given directed graph in which the maximum total degree (inplus out) is 3. For these graphs, we present: (i) a simple combinatorial algorithm that achieves an 11/12-approximation (the previous best factor was 2/3 [1]), (ii) a lower bound of 125/126 on approximability, and (iii) an approximation-preserving reduction from the general case: if for any ε > 0, there exists a (17/18 + ε)-approximation algorithm for the maximum acyclic subgraph problem in graphs with maximum degree 3, then there is a (1/2 + δ)-approximation algorithm for general graphs for some δ > 0. The problem of finding a better-than-half approximation for general graphs is open.

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References

  1. Bonnie Berger and Peter W. Shor. Tight Bounds on the Maximum Acyclic Subgraph Problem, Journal of Algorithms, vol. 25, pages 1–18, 1997.

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  2. Richard M Karp. Reducibility Among Combinatorial Problems, Complexity of Computer Computations, Plenum Press, 1972.

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  3. Fang Chen and László Lovász. Personal communication via Santosh Vempala.

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  4. Alantha Newman. Approximating the Maximum Acyclic Subgraph, M.S. Thesis,MIT, June 2000.

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  5. Alantha Newman and Santosh Vempala. Fences Are Futile: On Relaxations for the Linear Ordering Problem, Proceedings of IPCO 2001, Springer-Verlag.

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Author information

Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139

    Alantha Newman

Authors
  1. Alantha Newman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, MIT, Cambridge, MA, 02139, USA

    Michel Goemans

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, Université de Genéve, 24, Rue General Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  4. Computer Science Division, University of California at Berkeley, 615 Soda Hall, Berkeley, CA, 94720-1776, USA

    Luca Trevisan

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© 2001 Springer-Verlag Berlin Heidelberg

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Newman, A. (2001). The Maximum Acyclic Subgraph Problem and Degree-3 Graphs. In: Goemans, M., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. RANDOM APPROX 2001 2001. Lecture Notes in Computer Science, vol 2129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44666-4_18

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  • DOI: https://doi.org/10.1007/3-540-44666-4_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42470-3

  • Online ISBN: 978-3-540-44666-8

  • eBook Packages: Springer Book Archive

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