Tight approximability results for test set problems in bioinformatics

Piotr Berman, Bhaskar DasGupta*, Ming-Yang Kao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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. 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.

Original languageEnglish (US)
Pages (from-to)145-162
Number of pages18
JournalJournal of Computer and System Sciences
Volume71
Issue number2
DOIs
StatePublished - Aug 2005

Keywords

  • Approximation algorithms
  • Lower Bounds
  • Minimum cost probe set problems
  • String Barcoding
  • Test set problems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics

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