TY - GEN

T1 - Restricted common superstring and restricted common supersequence

AU - Clifford, Raphaël

AU - Gotthilf, Zvi

AU - Lewenstein, Moshe

AU - Popa, Alexandru

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - The shortest common superstring and the shortest common supersequence are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the Restricted Common Superstring (shortly RCSstr) problem and the Restricted Common Supersequence (shortly RCSseq). In the RCSstr (RCSseq) problem we are given a set S of n strings, s 1, s 2, ..., s n , and a multiset t = {t 1, t 2, ..., t m }, and the goal is to find a permutation π: {1, ..., m} → {1, ..., m} to maximize the number of strings in S that are substrings (subsequences) of π(t) = t π(1) t π(2) ⋯ t π(m) (we call this ordering of the multiset, π(t), a permutation of t). We first show that in its most general setting the RCSstr problem is NP-complete and hard to approximate within a factor of n 1 - ε , for any ε > 0, unless P = NP. Afterwards, we present two separate reductions to show that the RCSstr problem remains NP-Hard even in the case where the elements of t are drawn from a binary alphabet or for the case where all input strings are of length two. We then present some approximation results for several variants of the RCSstr problem. In the second part of this paper, we turn to the RCSseq problem, where we present some hardness results, tight lower bounds and approximation algorithms.

AB - The shortest common superstring and the shortest common supersequence are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the Restricted Common Superstring (shortly RCSstr) problem and the Restricted Common Supersequence (shortly RCSseq). In the RCSstr (RCSseq) problem we are given a set S of n strings, s 1, s 2, ..., s n , and a multiset t = {t 1, t 2, ..., t m }, and the goal is to find a permutation π: {1, ..., m} → {1, ..., m} to maximize the number of strings in S that are substrings (subsequences) of π(t) = t π(1) t π(2) ⋯ t π(m) (we call this ordering of the multiset, π(t), a permutation of t). We first show that in its most general setting the RCSstr problem is NP-complete and hard to approximate within a factor of n 1 - ε , for any ε > 0, unless P = NP. Afterwards, we present two separate reductions to show that the RCSstr problem remains NP-Hard even in the case where the elements of t are drawn from a binary alphabet or for the case where all input strings are of length two. We then present some approximation results for several variants of the RCSstr problem. In the second part of this paper, we turn to the RCSseq problem, where we present some hardness results, tight lower bounds and approximation algorithms.

UR - http://www.scopus.com/inward/record.url?scp=79960081879&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-21458-5_39

DO - 10.1007/978-3-642-21458-5_39

M3 - Conference contribution

AN - SCOPUS:79960081879

SN - 9783642214578

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 467

EP - 478

BT - Combinatorial Pattern Matching - 22nd Annual Symposium, CPM 2011, Proceedings

T2 - 22nd Annual Symposium on Combinatorial Pattern Matching, CPM 2011

Y2 - 27 June 2011 through 29 June 2011

ER -