Locality in distributed graph algorithms
SIAM Journal on Computing
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Robust position-based routing in wireless Ad Hoc networks with unstable transmission ranges
DIALM '01 Proceedings of the 5th 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
Local approximation schemes for ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
The feasibility of matchings in a wireless network
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Local PTAS for Independent Set and Vertex Cover in Location Aware Unit Disk Graphs
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
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)
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We present 1 驴 驴approximation algorithms for the maximum matching problem in location aware unit disc graphs and in growth-bounded graphs. The algorithm for unit disk graph is local in the sense that whether or not an edge is in the matching depends only on other vertices which are at most a constant number of hops away from it. The algorithm for growth-bounded graphs needs at most $O\left(\log\triangle\log^{*}n\right.+$ $\left.\frac{1}{\epsilon}^{O(1)}\cdot\log^{*}n\right)$ communication rounds during its execution. Using these matching algorithms we can compute vertex covers of the respective graph classes whose size are at most twice the optimal.