Complexities of Efficient Solutions of Rectilinear Polygon Cover Problems

P. Berman, B. DasGupta

    Research output: Contribution to journalArticle

    22 Scopus citations

    Abstract

    The rectilinear polygon cover problem is one in which a certain class of features of a rectilinear polygon of n vertices has to be covered with the minimum number of rectangles included in the polygon. In particular, we consider covering the entire interior, the boundary, and the set of corners of the polygon. These problems have important applications in storing images and in the manufacture of integrated circuits. Unfortunately, most of these problems are known to be NP-complete. Hence it is necessary to develop efficient heuristics for these problems or to show that the design of efficient heuristics is impossible. In this paper we show: (a) The corner cover problem is NP-complete. (b) The boundary and the corner cover problem can be approximated within a ratio of 4 of the optimum in O(n logn) and O(n1.5) time, respectively. (c) No polynomial-time approximation scheme exists for the interior and the boundary cover problems, unless P = NP.

    Original languageEnglish (US)
    Pages (from-to)331-356
    Number of pages26
    JournalAlgorithmica (New York)
    Volume17
    Issue number4
    DOIs
    StatePublished - Apr 1997

    All Science Journal Classification (ASJC) codes

    • Computer Science(all)
    • Computer Science Applications
    • Applied Mathematics

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