13 research outputs found
On vertex independence number of uniform hypergraphs
Abstract
Let H be an r-uniform hypergraph with r ≥ 2 and let α(H) be its vertex independence number. In the paper bounds of α(H) are given for different uniform hypergraphs: if H has no isolated vertex, then in terms of the degrees, and for triangle-free linear H in terms of the order and average degree.</jats:p
Approximation Bounds For Minimum Degree Matching
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 we show that MINGREEDY achieves
approximation ratio at least 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.Comment: % 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 tigh