Abstract
Damian and Pemmaraju (2002) [8] introduced leaf sector covers for circle graphs and presented an O(n2)-time algorithm to find this data structure. They subsequently employed it as an algorithmic tool, leading to the development of an 8-approximation algorithm for the dominating set problem, a (2+ε)-approximation scheme for the dominating set problem, and a (3+ε)-approximation scheme for the total dominating set problem.In this paper, we have improved the time complexity from O(n2) to O(n+m) for finding a leaf sector cover. Furthermore, we employed leaf sector covers as a powerful algorithmic tool to design a 10-approximation algorithm for the total dominating set problem and a 12-approximation algorithm for the paired-dominating set problem. Moreover, we also proposed a (2+ε)-approximation scheme for the total dominating set problem and a (4+ε)-approximation scheme for the paired-dominating set problem. The results presented above are currently the best algorithms for circle graphs.
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.
