ICCSA 2007: Computational Science and Its Applications – ICCSA 2007 pp 96-109 | Cite as
Optimal Parameterized Rectangular Coverings
Abstract
Recently in [12] a deterministic worst-case upper bound was shown for the problem of covering a set of integer-coordinate points in the plane with axis-parallel rectgangles minimizing a certain objective function on rectangles. Because the rectangles have to meet a lower bound condition for their side lengths, this class of problems is termed 1-sided. The present paper is devoted to show that the bounds for solving this 1-sided problem class also hold for problem variants with 2-sided length constraints on coverings meaning that the rectangles are subjected also to an upper bound for side lengths. All these 2-sided variants are NP-hard. We also provide a generalization of the results to the d-dimensional case.
Keywords
parameterized rectangular covering optimization problem dynamic programming NP-hardness integer grid exact algorithmics closure operatorPreview
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