We present an efficient algorithm for solving an interval coverage problem. Given n intervals of the same length on a line L and a line segment B on L, we want to move the intervals along L such that every point of B is covered by at least one interval and the sum of the moving distances of all intervals is minimized. As a fundamental computational geometry problem, it has applications in mobile sensor barrier coverage in wireless sensor networks. The previous work gave an O(n2) time algorithm for it. In this thesis, by discovering many interesting observations and developing new algorithmic techniques, we present an O(nlogn) time algorithm for this problem. We also show that Ω(n log n) is the lower bound for the time complexity. Therefore, our algorithm is optimal. Further, our observations and algorithmic techniques may be useful for solving other related problems.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-4918 |
| Date | 01 May 2014 |
| Creators | Andrews, Aaron M. |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact Andrew Wesolek (andrew.wesolek@usu.edu). |
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