On approximation properties of the independent set problem for low degree graphs

P. Berman, T. Fujito

    Research output: Contribution to journalArticlepeer-review

    62 Scopus citations

    Abstract

    The subject of this paper is the Independent Set problem for bounded node degree graphs. It is shown that the problem remains MAX SNP-complete even when graphs are restricted to being of degree bounded by 3 or to being 3-regular. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. We next study a better polynomial time approximation of the problem for degree 3 graphs. The performance ratio is improved from the previous best of 5/4 to arbitrarily close to 6/5 for degree 3 graphs and to 7/6 for cubic graphs. When combined with existing techniques this result also leads to approximation ratios, (B + 3)/5 + ε for the independent set problem and 2 - 5/(B + 3) + ε for the vertex cover problem on graphs of degree B, improving previous bounds for relatively small odd B.

    Original languageEnglish (US)
    Pages (from-to)115-132
    Number of pages18
    JournalTheory of Computing Systems
    Volume32
    Issue number2
    DOIs
    StatePublished - 1999

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computational Theory and Mathematics

    Fingerprint

    Dive into the research topics of 'On approximation properties of the independent set problem for low degree graphs'. Together they form a unique fingerprint.

    Cite this