Approximation Bounds For Minimum Degree Matching

Bert Besser

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arXiv · 1408.0596

Approximation Bounds For Minimum Degree Matching

Bert Besser

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Abstract

We consider the MINGREEDY strategy for Maximum Cardinality Matching. MINGREEDY repeatedly selects an edge incident with a node of minimum degree. For graphs of degree at most $\Delta$ we show that MINGREEDY achieves approximation ratio at least $ \frac{\Delta-1}{2\Delta-3} $ in the worst case and that this performance is optimal among adaptive priority algorithms in the vertex model, which include many prominent greedy matching heuristics. Even when considering expected approximation ratios of randomized greedy strategies, no better worst case bounds are known for graphs of small degrees.

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Bert Besser. 2014-08-04. Approximation Bounds For Minimum Degree Matching. https://arxiv.org/abs/1408.0596

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