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Titlebook: Algorithms - ESA 2009; 17th Annual European Amos Fiat,Peter Sanders Conference proceedings 2009 Springer-Verlag Berlin Heidelberg 2009 Sche

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Output-Sensitive Algorithms for Enumerating Minimal Transversals for Some Geometric Hypergraphs following problems: (i) hitting hyper-rectangles by points in .; (ii) stabbing connected objects by axis-parallel hyperplanes in .; and (iii) hitting half-planes by points. For both the covering and hitting set versions, we obtain incremental polynomial-time algorithms, provided that the dimension . is fixed.
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https://doi.org/10.1007/978-3-642-91741-7 With the same running time, the algorithm can be generalized in two directions. The algoritm is a counting algorithm, and the same ideas can be used to count other objects. For example, one can count the number of independent sets of all possible sizes simultaneously with the same running time. The
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https://doi.org/10.1007/978-3-642-91741-7are adjacent and |.(.) − .(.)| ≥ 1 if . and . are at distance 2, for all . and . in .(.). A .-.(2,1)-labeling is an .(2,1)-labeling .:.(.)→{0,...,.}, and the .(2,1)-labeling problem asks the minimum ., which we denote by .(.), among all possible assignments. It is known that this problem is NP-hard
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Betriebswirtschaftliche Beiträge., . ≤ . ≤ .} where . has at most . nonzeroes per row, we give a .-approximation algorithm. (We assume ., ., ., . are nonnegative.) For any . ≥ 2 and .> 0, if . ≠ . this ratio cannot be improved to . − 1 − ., and under the unique games conjecture this ratio cannot be improved to . − .. One key idea
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