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International Journal of Distributed Sensor Networks
Volume 2012 (2012), Article ID 918252, 25 pages
http://dx.doi.org/10.1155/2012/918252
Research Article

The Complexity of the Minimum Sensor Cover Problem with Unit-Disk Sensing Regions over a Connected Monitored Region

Department of Computer Science and Information Engineering, National Chung Cheng University, 168 University Road, Min-Hsiung Chia-Yi 621, Taiwan

Received 17 June 2011; Revised 12 August 2011; Accepted 16 August 2011

Academic Editor: Yuhang Yang

Copyright © 2012 Ren-Song Ko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers the complexity of the Minimum Unit-Disk Cover (MUDC) problem. This problem has applications in extending the sensor network lifetime by selecting minimum number of nodes to cover each location in a geometric connected region of interest and putting the remaining nodes in power saving mode. MUDC is a restricted version of the well-studied Minimum Set Cover (MSC) problem where the sensing region of each node is a unit-disk and the monitored region is geometric connected, a well-adopted network model in many works of the literature. We first present the formal proof of its NP-completeness. Then we illustrate several related optimum problems under various coverage constraints and show their hardness results as a corollary. Furthermore, we propose an efficient algorithm for reducing MUDC to MSC which has many well-known algorithms for approximated solutions. Finally, we present a decentralized scalable algorithm with a guaranteed performance and a constant approximation factor algorithm if the maximum node density is fixed.