Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On the red-blue set cover problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
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Information Processing Letters
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On the Positive--Negative Partial Set Cover problem
Information Processing Letters
Improved approximating algorithms for Directed Steiner Forest
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Optimising topical query decomposition
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ACM Transactions on Algorithms (TALG)
An improved algorithm for the red-blue hitting set problem with the consecutive ones property
Information Processing Letters
New results on the complexity of the max- and min-rep problems
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Covering analysis of the greedy algorithm for partial cover
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Evader interdiction and collateral damage
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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This paper presents approximation algorithms for two extensions of the set cover problem: a graph-based extension known as the Max-Rep or Label-Cover"M"A"Xproblem, and a color-based extension known as the Red-Blue Set Cover problem. First, a randomized algorithm guaranteeing approximation ratio n with high probability is proposed for the Max-Rep (or Label-Cover"M"A"X) problem, where n is the number of vertices in the graph. This algorithm is then generalized into a 4n-ratio algorithm for the nonuniform version of the problem. Secondly, it is shown that the Red-Blue Set Cover problem can be approximated with ratio 2nlog@b, where n is the number of sets and @b is the number of blue elements. Both algorithms can be adapted to the weighted variants of the respective problems, yielding the same approximation ratios.