Abstract
We consider the problem of covering polygons, without any acute interior angles, with rectangles. The rectangles must lie entirely within the polygon and it is preferable to cover the polygon with as few rectangles as possible. Let P be an arbitrary hole-free input polygon, with n vertices, coverable by rectangles. Let μ(P) denote the minimum number of rectangles required to cover P. In this paper we show, by using new techniques, that it is possible to construct a covering within an O(α(n)) approximation factor in O(n+μ(P)) time, where α(n) is the extremely slowly growing inverse of Ackermann's function. This improves the Ω(n 0.49...) worst-case approximation factor in time O(n log n+μ(P)) known before.
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© 1997 Springer-Verlag Berlin Heidelberg
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Levcopoulos, C., Gudmundsson, J. (1997). A linear-time heuristic for minimum rectangular coverings (Extended abstract). In: Chlebus, B.S., Czaja, L. (eds) Fundamentals of Computation Theory. FCT 1997. Lecture Notes in Computer Science, vol 1279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036193
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DOI: https://doi.org/10.1007/BFb0036193
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