## Abstract

A test scheduling instance is specified by a set of elements, a set of tests, which are subsets of elements, and numeric priorities assigned to elements. The schedule is a sequence of test invocations with the goal of covering all elements. This formulation had been used to model problems in multiple application domains from network failure detection to broadcast scheduling. The modeling considered both SUM_{e} and MAX_{e} objectives, which correspond to average or worst-case cover times over elements (weighted by priority), and both one-time testing, where the goal is to detect if a fault is currently present, and continuous testing, performed in the background in order to detect presence of failures soon after they occur. Since all variants are NP hard, the focus is on approximations. We present combinatorial approximations algorithms for both SUM_{e} and MAX _{e} objectives on continuous and MAX_{e} on one-time schedules. The approximation ratios we obtain depend logarithmically on the number of elements and significantly improve over previous results. Moreover, our unified treatment of SUM_{e} and MAX_{e} objectives facilitates simultaneous approximation with respect to both. Since one-time and continuous testing can be viable alternatives, we study their relation, which captures the overhead of continuous testing. We establish that for both SUM_{e} and MAX_{e} objectives, the ratio of the optimal one-time to continuous cover times is O(log n), where n is the number of elements. We show that this is tight as there are instances with ratio Ω(log n). We provide evidence, however, by considering Zipf distributions, that the typical ratio is lower.

Original language | English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |

Subtitle of host publication | Algorithms and Techniques - 16th International Workshop, APPROX 2013 and 17th International Workshop, RANDOM 2013, Proceedings |

Pages | 81-95 |

Number of pages | 15 |

DOIs | |

State | Published - 2013 |

Event | 16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013 - Berkeley, CA, United States Duration: 21 Aug 2013 → 23 Aug 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8096 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013 |
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Country/Territory | United States |

City | Berkeley, CA |

Period | 21/08/13 → 23/08/13 |