Abstract
We consider the analysis of linear programming relaxations of a large class of combinatorial problems that can be formulated as problems of covering cuts, including the Steiner tree, the travelling salesman, the vehicle routing, the matching, the T-join and the survivable network design problem, to name a few. We prove that all of the problems in the class satisfy a nice structural property, the parsimonious property, generalizing earlier work by Goemans and Bertsimas (1993). We utilize the parsimonious property to establish worst-case bounds between the gap of the IP and LP values for the class of 0–1 proper functions, leading to a new 2-approximation algorithm for this class of problems. We also extend the parsimonious property to a class of cut-covering problems that model certain instances of the edge-disjoint path problem.
Sign-in/Register to access full text options 
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.
