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@article{Gamarnik2009RandomizedGA, title={Randomized greedy algorithms for independent sets and matchings in regular graphs: Exact results and finite girth corrections}, author={David Gamarnik and David A. Goldberg}, journal={Combinatorics, Probability & Computing}, year={2009}, volume={19}, pages={61-85} }

- Published in Combinatorics, Probability & Computing 2009
DOI:10.1017/S0963548309990186

We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for r-regular graphs with n nodes and girth at least g, the algorithm finds an independent set of expected cardinality f(r)n−O ( (r−1) g2 g 2 ! n ) , where f(r) is a function which we explicitly compute. A similar result is established for matchings. Our results imply improved bounds for the size of the largest independent set in… CONTINUE READING