TY - JOUR
T1 - Tight approximability results for test set problems in bioinformatics
AU - Berman, Piotr
AU - DasGupta, Bhaskar
AU - Kao, Ming Yang
N1 - Funding Information:
A preliminary version of these results appeared in: T. Hagerup, J. Katajainen (Eds.), Nineth Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science, vol. 3111, Springer, July 2004, pp. 39–50. ∗Corresponding author. E-mail addresses: berman@cse.psu.edu (P. Berman), dasgupta@cs.uic.edu (B. DasGupta), kao@cs.northwestern.edu (M.-Y. Kao). 1Supported by NSF Grant CCR-0208821. 2Supported in part by NSF Grants CCR-0296041, CCR-0206795, CCR-0208749 and a CAREER Grant IIS-0346973. 3Supported in part by NSF Grant EIA-0112934.
PY - 2005/8
Y1 - 2005/8
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jcss.2005.02.001
DO - 10.1016/j.jcss.2005.02.001
M3 - Article
AN - SCOPUS:21144442727
SN - 0022-0000
VL - 71
SP - 145
EP - 162
JO - Journal of Computer and System Sciences
JF - Journal of Computer and System Sciences
IS - 2
ER -