Abstract
We present 1 − ε 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.
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Wiese, A., Kranakis, E. (2008). Local Maximal Matching and Local 2-Approximation for Vertex Cover in UDGs. In: Coudert, D., Simplot-Ryl, D., Stojmenovic, I. (eds) Ad-hoc, Mobile and Wireless Networks. ADHOC-NOW 2008. Lecture Notes in Computer Science, vol 5198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85209-4_1
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DOI: https://doi.org/10.1007/978-3-540-85209-4_1
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