An improved approximation algorithm for the complementary maximal strip recovery problem

Given two genomic maps G₁ and G₂ 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 G₁ and G₂ 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 7/3-approximation algorithm for the CMSR problem, with its worst-case performance analysis done through a local amortization with a re-weighting scheme.