## 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) |
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Pages (from-to) | 39-50 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 3111 |

State | Published - Dec 1 2004 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)