Motivated by comparative genomics, Chen et al. [9] introduced the Maximum
Duo-preservation String Mapping (MDSM) problem in which we are given two
strings s1β and s2β from the same alphabet and the goal is to find a
mapping Ο between them so as to maximize the number of duos preserved. A
duo is any two consecutive characters in a string and it is preserved in the
mapping if its two consecutive characters in s1β are mapped to same two
consecutive characters in s2β. The MDSM problem is known to be NP-hard and
there are approximation algorithms for this problem [3, 5, 13], but all of them
consider only the "unweighted" version of the problem in the sense that a duo
from s1β is preserved by mapping to any same duo in s2β regardless of their
positions in the respective strings. However, it is well-desired in comparative
genomics to find mappings that consider preserving duos that are "closer" to
each other under some distance measure [19]. In this paper, we introduce a
generalized version of the problem, called the Maximum-Weight Duo-preservation
String Mapping (MWDSM) problem that captures both duos-preservation and
duos-distance measures in the sense that mapping a duo from s1β to each
preserved duo in s2β has a weight, indicating the "closeness" of the two
duos. The objective of the MWDSM problem is to find a mapping so as to maximize
the total weight of preserved duos. In this paper, we give a polynomial-time
6-approximation algorithm for this problem.Comment: Appeared in proceedings of the 23rd International Computing and
Combinatorics Conference (COCOON 2017