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.
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Porschen, S. (2007). Optimal Parameterized Rectangular Coverings. In: Gervasi, O., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2007. ICCSA 2007. Lecture Notes in Computer Science, vol 4705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74472-6_8
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DOI: https://doi.org/10.1007/978-3-540-74472-6_8
Publisher Name: Springer, Berlin, Heidelberg
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