Randomized algorithms
Various notions of approximations: good, better, best, and more
Approximation algorithms for NP-hard problems
Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles)
Discrete Applied Mathematics - Special volume on computational molecular biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
Label placement by maximum independent set in rectangles
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Simple approximation algorithm for nonoverlapping local alignments
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
On Some Tighter Inapproximability Results
On Some Tighter Inapproximability Results
Efficient Amplifiers and Bounded Degree Optimization
Efficient Amplifiers and Bounded Degree Optimization
Inapproximability of maximal strip recovery
Theoretical Computer Science
ACM Transactions on Algorithms (TALG)
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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{((2k - 1)/((k + 1)2k - 1))Lk,3, ((2k - 1)/((2k + 1)2k - 1))Lk,6} is a lower bound of the worst-case relative error of the problem, where Lk,3 and Lk,6 are the lower bounds of the worst-case relative error of MAX kSAT-3 and MAX kSAT-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.