Improved approximations of packing and covering problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Algorithms for choosing differential gene expression experiments
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
String barcoding: uncovering optimal virus signatures
Proceedings of the sixth annual international conference on Computational biology
On the Approximability of the Minimum Test Collection Problem
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Non-unique probe selection and group testing
Theoretical Computer Science
Approximating the online set multicover problems via randomized winnowing
Theoretical Computer Science
Faster Algorithm for the Set Variant of the String Barcoding Problem
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
On approximation complexity of metric dimension problem
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Approximation complexity of Metric Dimension problem
Journal of Discrete Algorithms
A tighter analysis of set cover greedy algorithm for test set
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
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In this paper, we investigate the test set problem and its variations that appear in a variety of applications. In general, we are given a universe of objects to be ''distinguished'' by a family of ''tests'', and we want to find the smallest sufficient collection of tests. In the simplest version, a test is a subset of the universe and two objects are distinguished by our collection if one test contains exactly one of them. Variations allow tests to be multi-valued functions or unions of ''basic'' tests, and different notions of the term distinguished. An important version of this problem that has applications in DNA sequence analysis has the universe consisting of strings over a small alphabet and tests that are detecting presence (or absence) of a substring. For most versions of the problem, including the latter, we establish matching lower and upper bounds on approximation ratio. When tests can be formed as unions of basic tests, we show that the problem is as hard as the graph coloring problem. We conclude by reporting preliminary computational results on the implementations of our algorithmic approaches for the minimum cost probe set problems on a data set used by Borneman et al.