An exponential time 2-approximation algorithm for bandwidth

Martin Fürer, Serge Gaspers, Shiva Prasad Kasiviswanathan

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    14 Scopus citations

    Abstract

    The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b. In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797 n) = O(3 0.6217n) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have an O*(3 n) and O*(2 n) worst-case time bounds, respectively. Our algorithm is based on constructing bucket decompositions of the input graph. A bucket decomposition partitions the vertex set of a graph into ordered sets (called buckets) of (almost) equal sizes such that all edges are either incident on vertices in the same bucket or on vertices in two consecutive buckets. The idea is to find the smallest bucket size for which there exists a bucket decomposition. The algorithm uses a simple divide-and-conquer strategy along with dynamic programming to achieve this improved time bound.

    Original languageEnglish (US)
    Title of host publicationParameterized and Exact Computation - 4th International Workshop, IWPEC 2009, Revised Selected Papers
    Pages173-184
    Number of pages12
    DOIs
    StatePublished - Dec 24 2009
    Event4th International Workshop on Parameterized and Exact Computation, IWPEC 2009 - Copenhagen, Denmark
    Duration: Sep 10 2009Sep 11 2009

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume5917 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other4th International Workshop on Parameterized and Exact Computation, IWPEC 2009
    CountryDenmark
    CityCopenhagen
    Period9/10/099/11/09

      Fingerprint

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Fürer, M., Gaspers, S., & Kasiviswanathan, S. P. (2009). An exponential time 2-approximation algorithm for bandwidth. In Parameterized and Exact Computation - 4th International Workshop, IWPEC 2009, Revised Selected Papers (pp. 173-184). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5917 LNCS). https://doi.org/10.1007/978-3-642-11269-0_14