Discrete Mathematics - Topics on domination
Locality in distributed graph algorithms
SIAM Journal on Computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Message-optimal connected dominating sets in mobile ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Approximation algorithms for combinatorial problems
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Proceedings of the 2004 joint workshop on Foundations of mobile computing
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Local approximation schemes for ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
ADHOC-NOW'07 Proceedings of the 6th international conference on Ad-hoc, mobile and wireless networks
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
A PTAS for the minimum dominating set problem in unit disk graphs
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Analysing local algorithms in location-aware quasi-unit-disk graphs
Discrete Applied Mathematics
ACM Computing Surveys (CSUR)
Hi-index | 0.00 |
We present local 1 + ε approximation algorithms for the minimum dominating and the connected dominating set problems in location aware Unit Disk Graphs (UDGs). Our algorithms are local in the sense that the status of a vertex v in the output (i.e. whether or not v is part of the set to be computed) depends only on the vertices which are a constant number of edges (hops) away from v. This constant is independent of the size of the network. In our graph model we assume that each vertex knows its geographic coordinates in the plane (location aware nodes). Our algorithms give the best approximation ratios known for this setting. Moreover, the processing time that each vertex needs to determine whether or not it is part of the computed set is bounded by a polynomial in the number of vertices which are a constant number of hops away from it. We employ a new method for constructing the connected dominating set and we give the first analysis of trade-offs between approximation ratio and locality distance.