Close Approximations of Minimum Rectangular Coverings

Christos Levcopoulos, Joachim Gudmundsson

    Research output: Contribution to journalArticlepeer-review


    We consider the problem of covering arbitrary polygons with rectangles. The rectangles must lie entirely within the polygon. (This requires that the interior angles of the polygon are all greater than or equal to 90 degrees.) We want to cover the polygon with as few rectangles as possible. This problem has an application in fabricating masks for integrated circuits.
    In this paper we will describe the first polynomial algorithm, guaranteeing an O(log n) approximation factor, provided that the n vertices of the input polygon are given as polynomially bounded integer coordinates. By the same technique we also obtain the first algorithm producing a covering which is within a constant factor of the optimal in exponential time (compared to the doubly-exponential known before).
    Original languageEnglish
    Pages (from-to)437-452
    JournalJournal of Combinatorial Optimization
    Issue number4
    Publication statusPublished - 1999

    Subject classification (UKÄ)

    • Computer Science


    • computational geometry
    • covering polygons
    • approximation algorithms


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