The design and analysis of algorithms
The design and analysis of algorithms
Note on the independence number of triangle-free graphs, II
Journal of Combinatorial Theory Series A
A (&Dgr;/2)-approximation algorithm for the maximum independent set problem
Information Processing Letters
Improved non-approximability results
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Greed is good: approximating independent sets in sparse and bounded-degree graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximating maximum independent set in bounded degree graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximations of Independent Sets in Bounded-Degree Graphs
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
A survey of approximately optimal solutions to some covering and packing problems
ACM Computing Surveys (CSUR)
The algorithmic aspects of uncrowded hypergraphs
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
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
A note on the Greedy algorithm for finding independent sets of Ck-free graphs
Information Processing Letters
Combinatorics, Probability and Computing
Approximations of weighted independent set and hereditary subset problems
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
The greedier the better: an efficient algorithm for approximating maximum independent set
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Approximation algorithms for the weighted independent set problem
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
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Finding maximum independent sets in graphs with bounded maximum degree Δ is a well-studied NP-complete problem. We introduce an algorithm schema for improving the approximation of algorithms for this problem, which is based on preprocessing the input by removing cliques.We give an implementation of a theorem on the independence number of clique-free graphs, and use it to obtain an O(Δ/log log Δ) performance ratio with our schema. This is the first o(Δ) ratio for the independent set problem. We also obtain an efficient method with a Δ/6(1 + o(1)) performance ratio, improving on the best performance ratio known for intermediate values of Δ.