eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-06-30
14:1
14:13
10.4230/LIPIcs.CPM.2017.14
article
The Longest Filled Common Subsequence Problem
Castelli, Mauro
Dondi, Riccardo
Mauri, Giancarlo
Zoppis, Italo
Inspired by a recent approach for genome reconstruction from incomplete data, we consider a variant of the longest common subsequence problem for the comparison of two sequences, one of which is incomplete, i.e. it has some missing elements. The new combinatorial problem, called Longest Filled Common Subsequence, given two sequences A and B, and a multiset M of symbols missing in B, asks for a sequence B* obtained by inserting the symbols of M into B so that B* induces a common subsequence with A of maximum length. First, we investigate the computational and approximation complexity of the problem and we show that it is NP-hard and APX-hard when A contains at most two occurrences of each symbol. Then, we give a 3/5 approximation algorithm for the problem. Finally, we present a fixed-parameter algorithm, when the problem is parameterized by the number of symbols inserted in B that "match" symbols of A.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol078-cpm2017/LIPIcs.CPM.2017.14/LIPIcs.CPM.2017.14.pdf
longest common subsequence
approximation algorithms
computational complexity
fixed-parameter algorithms