English

Approximation Bounds For Minimum Degree Matching

Data Structures and Algorithms 2015-11-03 v3

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 Δ\Delta we show that MINGREEDY achieves approximation ratio at least Δ12Δ3 \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.

Keywords

Cite

@article{arxiv.1408.0596,
  title  = {Approximation Bounds For Minimum Degree Matching},
  author = {Bert Besser},
  journal= {arXiv preprint arXiv:1408.0596},
  year   = {2015}
}

Comments

% 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

R2 v1 2026-06-22T05:19:38.313Z