Tight approximability results for test set problems in bioinformatics

Piotr Berman; Bhaskar DasGupta; Ming Yang Kao

doi:10.1007/978-3-540-27810-8_5

Tight approximability results for test set problems in bioinformatics

Piotr Berman, Bhaskar DasGupta, Ming Yang Kao

Research output: Chapter in Book/Report/Conference proceeding › Chapter

5 Citations (SciVal)

Abstract

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.

Original language	English (US)
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Torben Hagerup, Jyrki Katajainen
Publisher	Springer Verlag
Pages	39-50
Number of pages	12
ISBN (Electronic)	3540223398, 9783540223399
DOIs	https://doi.org/10.1007/978-3-540-27810-8_5
State	Published - 2004

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3111
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-27810-8_5

Cite this

Berman, P., DasGupta, B., & Kao, M. Y. (2004). Tight approximability results for test set problems in bioinformatics. In T. Hagerup, & J. Katajainen (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 39-50). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3111). Springer Verlag. https://doi.org/10.1007/978-3-540-27810-8_5

Berman, Piotr ; DasGupta, Bhaskar ; Kao, Ming Yang. / Tight approximability results for test set problems in bioinformatics. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Torben Hagerup ; Jyrki Katajainen. Springer Verlag, 2004. pp. 39-50 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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.",

author = "Piotr Berman and Bhaskar DasGupta and Kao, {Ming Yang}",

note = "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.",

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Berman, P, DasGupta, B & Kao, MY 2004, Tight approximability results for test set problems in bioinformatics. in T Hagerup & J Katajainen (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3111, Springer Verlag, pp. 39-50. https://doi.org/10.1007/978-3-540-27810-8_5

Tight approximability results for test set problems in bioinformatics. / Berman, Piotr; DasGupta, Bhaskar; Kao, Ming Yang.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Torben Hagerup; Jyrki Katajainen. Springer Verlag, 2004. p. 39-50 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3111).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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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 - 2004

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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.

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Berman P, DasGupta B, Kao MY. Tight approximability results for test set problems in bioinformatics. In Hagerup T, Katajainen J, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 39-50. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-27810-8_5

Tight approximability results for test set problems in bioinformatics

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