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- W2047993953 abstract "Let S be a set of weighted axis-parallel rectangles such that for each axis no projection of one rectangle properly contains that of another. Two rectangles are in conflict if two projections of the rectangles on an axis intersect. The problem we consider in this paper is to find a maximum weighted subset S ′⊆ S of rectangles such that any two rectangles in S ′ are not in conflict. In this paper, we show that max{((2 k −1)/(( k +1)2 k −1)) L k ,3 ,((2 k −1)/((2 k +1)2 k −1)) L k ,6 } is a lower bound of the worst-case relative error of the problem, where L k ,3 and L k ,6 are the lower bounds of the worst-case relative error of MAX k SAT-3 and MAX k SAT-6, respectively. From the current best lower bound of MAX 2SAT-3 due to Berman and Karpinski, it can be shown that it is NP-hard to approximate the problem to within relative error less than 3 8668 ." @default.
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- W2047993953 date "2004-03-01" @default.
- W2047993953 modified "2023-09-30" @default.
- W2047993953 title "Hardness of approximation for non-overlapping local alignments" @default.
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- W2047993953 doi "https://doi.org/10.1016/s0166-218x(03)00344-5" @default.
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