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. (2018) provide an approximation algorithm with ratio Δ for the weighted version of the induced matching problem on graphs of maximum degree Δ. Their approach is based on an integer linear programming formulation whose integrality gap is at least Δ−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 58Δ+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−ϵ)Δ+12 for general Δ with ϵ≈0.02005, and 73 for Δ=3. Furthermore, we prove a best-possible bound on the fractional induced matching number in terms of the order and the maximum degree.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
