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ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
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Discrete Applied Mathematics - Special issue: Efficient algorithms
Non-independent randomized rounding and coloring
Discrete Applied Mathematics - Special issue: Efficient algorithms
The structure and number of global roundings of a graph
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COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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In this paper, we discuss the problem of computing an optimal rounding of a real sequence (resp. matrix) into an integral sequence (resp. matrix). Our criterion of the optimality is to minimize the weighted l∞-distance Dist∞F, w (A, B) between an input sequence (resp. matrix) A and the output B. The distance is dependent on a family F of intervals (resp. rectangular regions) for the sequence rounding (resp. matrix rounding) and positive-valued weight function w on the family. We give efficient polynomial-time algorithms for the sequence-rounding problem for weighted l∞-distance with respect to any weight function w and any family F of intervals. For the matrix-rounding problem, we prove that it is NP-hard to compute an approximate solution with approximation ratio smaller than 2 with respect to the unweighted l∞-distance associated with the family W2 of all 2 × 2 square regions.