Abstract
Given a directed acyclic graph and a set of vertex pairs, an antisymmetric path is a directed path that does not contain vertices from the same pair in the set. The goal of the Longest Antisymmetric Path problem is to determine the longest antisymmetric path that connects two given vertices in the graph. The problem has important applications in software testing and bioinformatics. The problem is known to be NP-hard. In this paper, we study the computational lower bound of the problem, we show that the problem cannot be solved in time 2o(n13) unless 3SAT can be solved in subexponential time. In addition, we study the inapproximability of the problem and show that the problem cannot be approximated within a ratio of (n−2)2 in polynomial time unless P=NP. Our technique also suggests that both the lower bound and inapproximability also hold for directed acyclic graphs of degree at most 6.
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.
