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Algorithms 2008, 1(1), 2-29; doi:10.3390/a1010002
Article

Impact of Locality on Location Aware Unit Disk Graphs

1,*  and 2,*
1 Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany 2 School of Computer Science, Carleton University 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada
* Authors to whom correspondence should be addressed.
Received: 15 August 2008 / Accepted: 4 September 2008 / Published: 12 September 2008
Download PDF [276 KB, uploaded 27 September 2008]

Abstract

Due to their importance for studies oi wireless networks, recent years have seen a surge of activity on the design of local algorithms for the solution of a variety of network tasks. We study the behaviour of algorithms with very low localities. Despite of this restriction we propose local constant ratio approximation algorithms for solving minimum dominating and connected dominating set, maximum independent set and minimum vertex cover in location aware Unit Disk Graphs. We also prove the first ever lower bounds for local algorithms for these problems with a given locality in the location aware setting.
Keywords: Unit Disk Graphs; Location Awareness; Local Algorithms; Approximation Algorithms; Lower Bounds Unit Disk Graphs; Location Awareness; Local Algorithms; Approximation Algorithms; Lower Bounds
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.

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MDPI and ACS Style

Wiese, A.; Kranakis, E. Impact of Locality on Location Aware Unit Disk Graphs. Algorithms 2008, 1, 2-29.

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