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- W2903860279 abstract "A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018) 304-310) provide an approximation algorithm with ratio $Delta$ for the weighted version of the induced matching problem on graphs of maximum degree $Delta$. Their approach is based on an integer linear programming formulation whose integrality gap is at least $Delta-1$, that is, their approach offers only little room for improvement in the weighted case. For the unweighted case though, we conjecture that the integrality gap is at most $frac{5}{8}Delta+O(1)$, and that also the approximation ratio can be improved at least to this value. We provide primal-dual approximation algorithms with ratios $(1-epsilon) Delta + frac{1}{2}$ for general $Delta$ with $epsilon approx 0.02005$, and $frac{7}{3}$ for $Delta=3$. Furthermore, we prove a best-possible bound on the fractional induced matching number in terms of the order and the maximum degree." @default.
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- W2903860279 date "2018-12-14" @default.
- W2903860279 modified "2023-09-23" @default.
- W2903860279 title "Linear programming based approximation for unweighted induced matchings --- breaking the $Delta$ barrier" @default.
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