An improved approximation algorithm for the complementary maximal strip recovery problem

Given two genomic maps G1G1 and G2G2 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 G1G1 and G2G2 such that the resultant subsequences, denoted as G1⁎ and G2⁎, can be partitioned into the same set of maximal strips, which are common substrings of length greater than or equal to two. The complementary   maximal strip recovery (CMSR) problem has the complementary goal to delete the minimum number of markers. Both MSR and CMSR have been shown to be NP-hard and APX-complete, and they admit a 4-approximation and a 3-approximation respectively. In this paper, we present an improved 73-approximation algorithm for the CMSR problem, with its worst-case performance analysis done through a local amortization with a re-weighting scheme.

► An improved 7/3-approximation algorithm is presented.
► It is a greedy algorithm using six operations at three levels of priority.
► Performance analysis is done through a re-weighting scheme and local amortization.
► The performance ratio is tight.