Discrete Mathematics - Topics on domination
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
On calculating connected dominating set for efficient routing in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Local approximation schemes for ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
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
A robust PTAS for maximum weight independent sets in unit disk graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
What can be approximated locally?: case study: dominating sets in planar graphs
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Local Maximal Matching and Local 2-Approximation for Vertex Cover in UDGs
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
Leveraging Linial's Locality Limit
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Polynomial kernels for hard problems on disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Minimum weight covering problems in stochastic environments
Information Sciences: an International Journal
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We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geographic coordinates in the plane (location aware nodes). Our algorithms are local in the sense that the status of each node v(whether or not vis in the computed set) depends only on the vertices which are a constant number of hops away from v. This constant is independent of the size of the network. We give upper bounds for the constant depending on the desired approximation ratio. We show that the processing time which is necessary in order to compute the status of a single vertex is bounded by a polynomial in the number of vertices which are at most a constant number of vertices away from it. Our algorithms give the best possible approximation ratios for this setting.The technique which we use to obtain the algorithm for vertex cover can also be employed for constructing the first global PTAS for this problem in unit disk graph which does not need the embedding of the graph as part of the input.