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Tighter Bounds on Feedback Vertex Sets in Mesh-Based Networks

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Structural Information and Communication Complexity (SIROCCO 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3104))

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Abstract

In this paper we consider the minimum feedback vertex set problem in graphs, i.e., the problem of finding a minimal cardinality subset of the vertices, whose removal makes a graph acyclic. The problem is \({\cal NP}\)-hard for general topologies, but optimal and near-optimal solutions have been provided for particular networks. We improve the upper bounds of [11] both for the two-dimensional mesh of trees, and for the pyramid networks. We also present upper and lower bounds for other topologies: the higher-dimensional meshes of trees, and the trees of meshes networks. For the two-dimensional meshes of trees the results are optimal; for the higher-dimensional meshes of trees and the tree of meshes the results are asymptotically optimal. For the pyramid networks, the presented upper bound almost matches the lower bound of [11].

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Università di Trieste, Italy

    Flaminia L. Luccio

  2. Institut für Informatik, Martin-Luther-Universität, Halle, Germany

    Jop F. Sibeyn

Authors
  1. Flaminia L. Luccio
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  2. Jop F. Sibeyn
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Research partially funded by grant APVV, 0433-06, Bratislava, Slovakia

    Ratislav Královic̆

  2. Department of Computer Science, University of Loughborough, Loughborough, UK

    Ondrej Sýkora

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© 2004 Springer-Verlag Berlin Heidelberg

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Luccio, F.L., Sibeyn, J.F. (2004). Tighter Bounds on Feedback Vertex Sets in Mesh-Based Networks. In: Královic̆, R., Sýkora, O. (eds) Structural Information and Communication Complexity. SIROCCO 2004. Lecture Notes in Computer Science, vol 3104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27796-5_19

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  • DOI: https://doi.org/10.1007/978-3-540-27796-5_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22230-9

  • Online ISBN: 978-3-540-27796-5

  • eBook Packages: Springer Book Archive

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