SIAM Journal on Discrete Mathematics
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
A still better performance guarantee for approximate graph coloring
Information Processing Letters
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Exact and Approximate Cut Covers of Graphs
On Exact and Approximate Cut Covers of Graphs
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Tight approximability results for test set problems in bioinformatics
Journal of Computer and System Sciences
On approximation complexity of metric dimension problem
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
network discovery and verification
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
An improved branch-and-bound algorithm for the test cover problem
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Approximation complexity of Metric Dimension problem
Journal of Discrete Algorithms
Parameterized study of the test cover problem
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
(Non-)existence of polynomial kernels for the Test Cover problem
Information Processing Letters
Experiment selection for causal discovery
The Journal of Machine Learning Research
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The minimum test collection problem is defined as follows. Given a ground set S and a collection C of tests (subsets of S), find the minimum subcollection C′ of C such that for every pair of elements (x, y) in S there exists a test in C′ that contains exactly one of x and y. It is well known that the greedy algorithm gives a 1 + 2 ln n approximation for the test collection problem where n = |S|, the size of the ground set. In this paper, we show that this algorithm is close to the best possible, namely that there is no o(log n)-approximation algorithm for the test collection problem unless P = NP. We give approximation algorithms for this problem in the case when all the tests have a small cardinality, significantly improving the performance guarantee achievable by the greedy algorithm. In particular, for instances with test sizes at most k we derive an O(log k) approximation. We show APX-hardness of the version with test sizes at most two, and present an approximation algorithm with ratio 7/6 + Ɛ for any fixed Ɛ 0.