Abstract
We study the average-case behavior of algorithms for finding a maximal disjoint subset of a given set of rectangles. In the probability model, a random rectangle is the product of two independent random intervals, each being the interval between two points drawn uniformly at random from [0, 1]. We have proved that the expected cardinality of a maximal disjoint subset of n random rectangles has the tight asymptotic bound Θ (n 1/2). Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we have been able to show that Ω (n 1/2) and O ((n logd − − 1 n)1/2) are asymptotic lower and upper bounds. In addition, we can prove that Θ (n d/( d + 1)) is a tight asymptotic bound for the case of random cubes.
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References
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© 2000 Springer-Verlag Berlin Heidelberg
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Coffman, E.G., Lueker, G.S., Spencer, J., Winkler, P.M. (2000). Average-Case Analysis of Rectangle Packings. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_30
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DOI: https://doi.org/10.1007/10719839_30
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