Abstract
Given an undirected complete weighted graph \(G=(V,E)\) with nonnegative weight function obeying the triangle inequality, a set \(\{C_1,C_2,\) \(\ldots ,C_k\}\) of cycles is called a cycle cover if \(V \subseteq \bigcup _{i=1}^k V(C_i)\) and its cost is given by the maximum weight of the cycles. The Minimum Cycle Cover Problem (MCCP) aims to find a cycle cover of cost at most \(\lambda \) with the minimum number of cycles. We propose new LP relaxations for MCCP as well as its variants, called the Minimum Path Cover Problem (MPCP) and the Minimum Tree Cover Problem, where the cycles are replaced by paths or trees. Moreover, we give new LP relaxations for a special case of the rooted version of MCCP/MPCP and show that these LP relaxations have significantly better integrality gaps than the previous relaxations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.