Approaching the 5/4-approximation for rectilinear Steiner trees

Piotr Berman, Ulrich Fößmeier, Marek Karpinski, Michael Kaufmann, Alexander Zelikovsky

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

    3 Citations (Scopus)

    Abstract

    The rectilinear Steiner tree problem requires to find a shortest tree connecting a given set of terminal points in the plane with rectilinear distance. We show that the performance ratios of Zelikovsky’s[17] heuristic is between 1.3 and 1.3125 (before it was only bounded from above by 1.375), while the performance ratio of the heuristic of Berman and Ramaiyer[l] is at most 1.271 (while the previous bound was 1.347). Moreover, we provide (formula Presented)-time algorithms that satisfy these performance ratios.

    Original languageEnglish (US)
    Title of host publicationAlgorithms - ESA'94 - 2nd Annual European Symposium, Proceedings
    EditorsJan van Leeuwen
    PublisherSpringer Verlag
    Pages60-71
    Number of pages12
    ISBN (Print)9783540584346
    StatePublished - Jan 1 1994
    Event2nd Annual European Symposium on Algorithms, ESA 1994 - Utrecht, Netherlands
    Duration: Sep 26 1994Sep 28 1994

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume855 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other2nd Annual European Symposium on Algorithms, ESA 1994
    CountryNetherlands
    CityUtrecht
    Period9/26/949/28/94

    Fingerprint

    Steiner Tree
    Approximation
    Heuristics
    Steiner Tree Problem

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Berman, P., Fößmeier, U., Karpinski, M., Kaufmann, M., & Zelikovsky, A. (1994). Approaching the 5/4-approximation for rectilinear Steiner trees. In J. van Leeuwen (Ed.), Algorithms - ESA'94 - 2nd Annual European Symposium, Proceedings (pp. 60-71). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 855 LNCS). Springer Verlag.
    Berman, Piotr ; Fößmeier, Ulrich ; Karpinski, Marek ; Kaufmann, Michael ; Zelikovsky, Alexander. / Approaching the 5/4-approximation for rectilinear Steiner trees. Algorithms - ESA'94 - 2nd Annual European Symposium, Proceedings. editor / Jan van Leeuwen. Springer Verlag, 1994. pp. 60-71 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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    abstract = "The rectilinear Steiner tree problem requires to find a shortest tree connecting a given set of terminal points in the plane with rectilinear distance. We show that the performance ratios of Zelikovsky’s[17] heuristic is between 1.3 and 1.3125 (before it was only bounded from above by 1.375), while the performance ratio of the heuristic of Berman and Ramaiyer[l] is at most 1.271 (while the previous bound was 1.347). Moreover, we provide (formula Presented)-time algorithms that satisfy these performance ratios.",
    author = "Piotr Berman and Ulrich F{\"o}{\ss}meier and Marek Karpinski and Michael Kaufmann and Alexander Zelikovsky",
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    Berman, P, Fößmeier, U, Karpinski, M, Kaufmann, M & Zelikovsky, A 1994, Approaching the 5/4-approximation for rectilinear Steiner trees. in J van Leeuwen (ed.), Algorithms - ESA'94 - 2nd Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 855 LNCS, Springer Verlag, pp. 60-71, 2nd Annual European Symposium on Algorithms, ESA 1994, Utrecht, Netherlands, 9/26/94.

    Approaching the 5/4-approximation for rectilinear Steiner trees. / Berman, Piotr; Fößmeier, Ulrich; Karpinski, Marek; Kaufmann, Michael; Zelikovsky, Alexander.

    Algorithms - ESA'94 - 2nd Annual European Symposium, Proceedings. ed. / Jan van Leeuwen. Springer Verlag, 1994. p. 60-71 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 855 LNCS).

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

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    AU - Zelikovsky, Alexander

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    N2 - The rectilinear Steiner tree problem requires to find a shortest tree connecting a given set of terminal points in the plane with rectilinear distance. We show that the performance ratios of Zelikovsky’s[17] heuristic is between 1.3 and 1.3125 (before it was only bounded from above by 1.375), while the performance ratio of the heuristic of Berman and Ramaiyer[l] is at most 1.271 (while the previous bound was 1.347). Moreover, we provide (formula Presented)-time algorithms that satisfy these performance ratios.

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    Berman P, Fößmeier U, Karpinski M, Kaufmann M, Zelikovsky A. Approaching the 5/4-approximation for rectilinear Steiner trees. In van Leeuwen J, editor, Algorithms - ESA'94 - 2nd Annual European Symposium, Proceedings. Springer Verlag. 1994. p. 60-71. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).