## Abstract

We study variants of the Strip Cover problem (SC) in which sensors with limited battery power are deployed on a line barrier, and the goal is to cover the barrier as long as possible. The energy consumption of a sensor depends on its sensing radius: energy is drained in inverse proportion to the sensor radius raised to a constant exponent α≥ 1. In the Set Once Strip Cover (OnceSC) the radius of each sensor can be set once, and the sensor can be activated at any time. SC_{k} and ONCESCk are variants of SC and OnceSC, resp., in which each sensor is associated with a set of at most k predetermined radii. It was previously known that OnceSC is NP-hard when α=1, and the complexity of the case where α> 1 remained open. We extend the above mentioned NP-hardness result in two ways: we show that OnceSC is NP-hard for every α> 1 and that OnceSC is strongly NP-hard for α=1. In addition, we show that ONCESCk, for k≥ 2, is NP-hard, for any α≥ 1, even for uniform radii sets. On the positive side, we present (i) a 5 γ^{α}-approximation algorithm for ONCESCk, for k≥ 1, where γ is the maximum ratio between two radii associated with the same sensor; (ii) a 5-approximation algorithm for SC_{k}, for every k≥1; and (iii) a 5 · 2^{α}-approximation algorithm for Strip Cover. Finally, we present an O(nlog n)-time algorithm for a variant of ONCESCk in which all sensors must be activated at the same time.

Original language | English |
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Title of host publication | Algorithms for Sensor Systems - 13th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2017, Revised Selected Papers |

Editors | Miguel A. Mosteiro, Tomasz Jurdzinski, Antonio Fernandez Anta, Yanyong Zhang |

Publisher | Springer Verlag |

Pages | 198-210 |

Number of pages | 13 |

ISBN (Print) | 9783319727509 |

DOIs | |

State | Published - 2017 |

Event | 13th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2017 - Vienna, Austria Duration: 4 Sep 2017 → 8 Sep 2017 |

### 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 | 10718 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 13th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2017 |
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Country/Territory | Austria |

City | Vienna |

Period | 4/09/17 → 8/09/17 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing AG 2017.

### Funding

D. Rawitz—Supported by the Israel Science Foundation (grant no. 497/14).

Funders | Funder number |
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Israel Science Foundation | 497/14 |