An optimisation algorithm for maximum independent set with applications in map labelling

B. Verweij, K.I. Aardal

    Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

    23 Citaten (Scopus)

    Samenvatting

    We consider the following map labelling problem: given distinct points p 1, p 2,...,p n in the plane, find a set of pairwise disjoint axis-parallel squares Q 1,Q 2,...,Q n where p i is a corner of Q i . This problem reduces to that of finding a maximum independent set in a graph. We present a branch and cut algorithm for finding maximum independent sets and apply it to independent set instances arising from map labelling. The algorithm uses a new technique for setting variables in the branch and bound tree that implicitly exploits the Euclidean nature of the independent set problems arising from map labelling. Computational experiments show that this technique contributes to controlling the size of the branch and bound tree. We also present a novel variant of the algorithm for generating violated odd-hole inequalities. Using our algorithm we can find provably optimal solutions for map labelling instances with up to 950 cities within modest computing time, a considerable improvement over the results reported on in the literature.
    Originele taal-2Engels
    TitelAlgorithms - ESA'99 : Proceedings 7th annual European symposium, Prague, Czech Republic, july 16-18, 1999
    RedacteurenJ. Nesetril
    UitgeverijSpringer
    Pagina's426-437
    ISBN van geprinte versie3-540-66251-0
    DOI's
    StatusGepubliceerd - 1999

    Publicatie series

    NaamLecture Notes in Computer Science
    Volume1643
    ISSN van geprinte versie0302-9743

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