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Approximating maximum independent sets by excluding subgraphs. (English) Zbl 0761.68044
Summary: An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known to \(O(n/(\log n)^ 2)\). We also obtain the same performance guarantee for graph coloring. The results can be combined into a surprisingly strong simultaneous performance guarantee for the clique and coloring problems.
The framework of subgraph-excluding algorithms is presented. We survey the known approximation algorithm for the independent set (clique), coloring, and vertex cover problems and show how almost all fit into that framework. We show that among subgraph-excluding algorithms, the ones presented achieve the optimal asymptotic performance guarantees.

MSC:
68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
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