On approximation properties of the independent set problem for degree 3 graphs

Piotr Berman, Toshihiro Fujito

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

    65 Citations (Scopus)

    Abstract

    The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SJVP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, |, to arbitrarily close to |. This result also provides improved poly-time approximation ratios, (Formula Presented), for odd degree B.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings
    EditorsSelim G. Akl, Frank Dehne, Jörg-Rüdiger Sack, Nicola Santoro
    PublisherSpringer Verlag
    Pages449-460
    Number of pages12
    ISBN (Print)3540602208, 9783540602200
    DOIs
    StatePublished - Jan 1 1995
    Event4th Workshop on Algorithms and Data Structures, WADS 1995 - Kingston, Canada
    Duration: Aug 16 1995Aug 18 1995

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume955
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other4th Workshop on Algorithms and Data Structures, WADS 1995
    CountryCanada
    CityKingston
    Period8/16/958/18/95

    Fingerprint

    Approximation Property
    Independent Set
    Graph in graph theory
    Approximation
    Maximum Degree
    Lowest
    Odd

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Berman, P., & Fujito, T. (1995). On approximation properties of the independent set problem for degree 3 graphs. In S. G. Akl, F. Dehne, J-R. Sack, & N. Santoro (Eds.), Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings (pp. 449-460). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955). Springer Verlag. https://doi.org/10.1007/3-540-60220-8_84
    Berman, Piotr ; Fujito, Toshihiro. / On approximation properties of the independent set problem for degree 3 graphs. Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. editor / Selim G. Akl ; Frank Dehne ; Jörg-Rüdiger Sack ; Nicola Santoro. Springer Verlag, 1995. pp. 449-460 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    @inproceedings{26c837a2b20a4912a95626f78867c381,
    title = "On approximation properties of the independent set problem for degree 3 graphs",
    abstract = "The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SJVP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, |, to arbitrarily close to |. This result also provides improved poly-time approximation ratios, (Formula Presented), for odd degree B.",
    author = "Piotr Berman and Toshihiro Fujito",
    year = "1995",
    month = "1",
    day = "1",
    doi = "10.1007/3-540-60220-8_84",
    language = "English (US)",
    isbn = "3540602208",
    series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
    publisher = "Springer Verlag",
    pages = "449--460",
    editor = "Akl, {Selim G.} and Frank Dehne and J{\"o}rg-R{\"u}diger Sack and Nicola Santoro",
    booktitle = "Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings",
    address = "Germany",

    }

    Berman, P & Fujito, T 1995, On approximation properties of the independent set problem for degree 3 graphs. in SG Akl, F Dehne, J-R Sack & N Santoro (eds), Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 955, Springer Verlag, pp. 449-460, 4th Workshop on Algorithms and Data Structures, WADS 1995, Kingston, Canada, 8/16/95. https://doi.org/10.1007/3-540-60220-8_84

    On approximation properties of the independent set problem for degree 3 graphs. / Berman, Piotr; Fujito, Toshihiro.

    Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. ed. / Selim G. Akl; Frank Dehne; Jörg-Rüdiger Sack; Nicola Santoro. Springer Verlag, 1995. p. 449-460 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955).

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

    TY - GEN

    T1 - On approximation properties of the independent set problem for degree 3 graphs

    AU - Berman, Piotr

    AU - Fujito, Toshihiro

    PY - 1995/1/1

    Y1 - 1995/1/1

    N2 - The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SJVP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, |, to arbitrarily close to |. This result also provides improved poly-time approximation ratios, (Formula Presented), for odd degree B.

    AB - The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SJVP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, |, to arbitrarily close to |. This result also provides improved poly-time approximation ratios, (Formula Presented), for odd degree B.

    UR - http://www.scopus.com/inward/record.url?scp=84958038732&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84958038732&partnerID=8YFLogxK

    U2 - 10.1007/3-540-60220-8_84

    DO - 10.1007/3-540-60220-8_84

    M3 - Conference contribution

    AN - SCOPUS:84958038732

    SN - 3540602208

    SN - 9783540602200

    T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

    SP - 449

    EP - 460

    BT - Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings

    A2 - Akl, Selim G.

    A2 - Dehne, Frank

    A2 - Sack, Jörg-Rüdiger

    A2 - Santoro, Nicola

    PB - Springer Verlag

    ER -

    Berman P, Fujito T. On approximation properties of the independent set problem for degree 3 graphs. In Akl SG, Dehne F, Sack J-R, Santoro N, editors, Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. Springer Verlag. 1995. p. 449-460. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-60220-8_84