Comparing incomplete sequences via longest common subsequence

Castelli, Mauro; Dondi, Riccardo; Mauri, Giancarlo; Zoppis, Italo

http://hdl.handle.net/10362/85834

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Resumo(s)

Inspired by scaffold filling, a recent approach for genome reconstruction from incomplete data, we consider a variant of the well-known longest common subsequence problem for the comparison of two sequences. The new problem, called Longest Filled Common Subsequence, aims to compare a complete sequence with an incomplete one, i.e. with some missing elements. Longest Filled Common Subsequence (LFCS), given a complete sequence A, an incomplete sequence 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. 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, and we give a polynomial time algorithm when the input sequences are over a constant-size alphabet. We give a [Formula presented] approximation algorithm for the Longest Filled Common Subsequence problem. Finally, we present a fixed-parameter algorithm for the problem, when it is parameterized by the number of symbols inserted in B that “match” symbols of A.

Descrição

Castelli, M., Dondi, R., Mauri, G., & Zoppis, I. (2019). Comparing incomplete sequences via longest common subsequence. Theoretical Computer Science, 796, 272-285. https://doi.org/10.1016/j.tcs.2019.09.022

Palavras-chave

Approximation algorithms Computational complexity Fixed-parameter algorithms Longest common subsequence String algorithms Theoretical Computer Science General Computer Science