On the independence number of sparse graphs
Random Structures & Algorithms
Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximating the independence number via the j -function
Mathematical Programming: Series A and B
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximations of Independent Sets in Graphs
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Inapproximability of Vertex Cover and Independent Set in Bounded Degree Graphs
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Distance approximation in bounded-degree and general sparse graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
SIAM Journal on Discrete Mathematics
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How well can the maximum size of an independent set, or the minimum size of a dominating set of a graph in which all degrees are at most d be approximated by a randomized constant time algorithm ? Motivated by results and questions of Nguyen and Onak, and of Parnas, Ron and Trevisan, we show that the best approximation ratio that can be achieved for the first question (independence number) is between ω(d/ log d) and O(d log log d/ log d), whereas the answer to the second (domination number) is (1 + o(1)) ln d.