TY - JOUR

T1 - Covering problems for partial words and for indeterminate strings

AU - Crochemore, M.

AU - Iliopoulos, Costas

AU - Kociumaka, T.

AU - Radoszewski, J.

AU - Rytter, W.

AU - Waleń, T.

PY - 2014

Y1 - 2014

N2 - © Springer International Publishing Switzerland 2014 We consider the problem of computing a solid cover of an indeterminate string. An indeterminate string may contain non-solid symbols, each of which specifies a subset of the alphabet that could be present at the corresponding position. We also consider covering partial words, which are a special case of indeterminate strings where each non-solid symbol is a don’t care symbol. We prove that both indeterminate string covering problem and partial word covering problem are NP-complete for binary alphabet and show that both problems are fixed-parameter tractable with respect to k, the number of non-solid symbols. For the indeterminate string covering problem we obtain a (Formula Presented)-time algorithm. For the partial word covering problem we obtain a (Formula Presented)-time algorithm.We prove that, unless the Exponential Time Hypothesis is false, no (Formula Presented)-time solution exists for this problem, which shows that our algorithm for this case is close to optimal. We also present an algorithm for both problems which is feasible in practice.

AB - © Springer International Publishing Switzerland 2014 We consider the problem of computing a solid cover of an indeterminate string. An indeterminate string may contain non-solid symbols, each of which specifies a subset of the alphabet that could be present at the corresponding position. We also consider covering partial words, which are a special case of indeterminate strings where each non-solid symbol is a don’t care symbol. We prove that both indeterminate string covering problem and partial word covering problem are NP-complete for binary alphabet and show that both problems are fixed-parameter tractable with respect to k, the number of non-solid symbols. For the indeterminate string covering problem we obtain a (Formula Presented)-time algorithm. For the partial word covering problem we obtain a (Formula Presented)-time algorithm.We prove that, unless the Exponential Time Hypothesis is false, no (Formula Presented)-time solution exists for this problem, which shows that our algorithm for this case is close to optimal. We also present an algorithm for both problems which is feasible in practice.

U2 - 10.1007/978-3-319-13075-018

DO - 10.1007/978-3-319-13075-018

M3 - Article

SN - 0302-9743

VL - 8889

SP - 220

EP - 232

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -