TY - GEN
T1 - Improved approximation results on the shortest common supersequence problem
AU - Gotthilf, Zvi
AU - Lewenstein, Moshe
PY - 2009
Y1 - 2009
N2 - The problem of finding the Shortest Common Supersequence (SCS) of an arbitrary number of input strings is a well-studied problem. Given a set L of k strings, s 1, s 2, ..., s k , over an alphabet ∑, we say that their SCS is the shortest string that contains each of the input strings as a subsequence. The problem is known to be NP-hard [8] even over binary alphabet [12]. In this paper we focus on approximating two NP-hard variants of the SCS problem. For the first variant, where all input strings are of length 2, we present a 2 - 2/1+log n log log n approximation algorithm, where |∑| = n. This result immediately improves the approximation algorithm presented in [17]. Moreover, we present a 7/6 (≈ 1.1666) approximation algorithm for the restricted variant (but still NP-hard) where all input strings are of length 2 and every character in ∑ has at most 3 occurrences in L.
AB - The problem of finding the Shortest Common Supersequence (SCS) of an arbitrary number of input strings is a well-studied problem. Given a set L of k strings, s 1, s 2, ..., s k , over an alphabet ∑, we say that their SCS is the shortest string that contains each of the input strings as a subsequence. The problem is known to be NP-hard [8] even over binary alphabet [12]. In this paper we focus on approximating two NP-hard variants of the SCS problem. For the first variant, where all input strings are of length 2, we present a 2 - 2/1+log n log log n approximation algorithm, where |∑| = n. This result immediately improves the approximation algorithm presented in [17]. Moreover, we present a 7/6 (≈ 1.1666) approximation algorithm for the restricted variant (but still NP-hard) where all input strings are of length 2 and every character in ∑ has at most 3 occurrences in L.
UR - http://www.scopus.com/inward/record.url?scp=70350635613&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-03784-9_27
DO - 10.1007/978-3-642-03784-9_27
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AN - SCOPUS:70350635613
SN - 3642037836
SN - 9783642037832
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 277
EP - 284
BT - String Processing and Information Retrieval - 16th International Symposium, SPIRE 2009, Proceedings
T2 - 16th International Symposium on String Processing and Information Retrieval, SPIRE 2009
Y2 - 25 August 2009 through 27 August 2009
ER -