Approximation Bounds For Minimum Degree Matching

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.

% CHANGELOG % rev 1 2014-12-02 % - Show that the class APV contains many prominent greedy matching algorithms. % - Adapt inapproximability bound for APV-algorithms to a priori knowledge on |V|. % rev 2 2015-10-31 % - improve performance guarantee of MINGREEDY to be tight

Cited by in corpus (1)

• On the Approximation Performance of Degree Heuristics for Matching