Abstract
Given two genomic maps G 1 and G 2 each represented as a sequence of n gene markers, the maximal strip recovery (MSR) problem is to retain the maximum number of markers in both G 1 and G 2 such that the resultant subsequences, denoted as \(G_{1}^{*}\) and \(G_{2}^{*}\), can be partitioned into the same set of maximal substrings of length greater than or equal to two. Such substrings can occur in the reversal and negated form. The complementary maximal strip recovery (CMSR) problem is to delete the minimum number of markers from both G 1 and G 2 for the same purpose, with its optimization goal exactly complementary to maximizing the total number of gene markers retained in the final maximal substrings. Both MSR and CMSR have been shown NP-hard and APX-hard. A 4-approximation algorithm is known for the MSR problem, but no constant ratio approximation algorithm for CMSR. In this paper, we present an O(3k n 2)-time fixed-parameter tractable (FPT) algorithm, where k is the size of the optimal solution, and a 3-approximation algorithm for the CMSR problem.
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.