TY - GEN

T1 - LCS approximation via embedding into local non-repetitive strings

AU - Landau, Gad M.

AU - Levy, Avivit

AU - Newman, Ilan

PY - 2009

Y1 - 2009

N2 - A classical measure of similarity between strings is the length of the longest common subsequence(LCS) between the two given strings. The search for efficient algorithms for finding the LCS has been going on for more than three decades. To date, all known algorithms may take quadratic time (shaved by logarithmic factors) to find large LCS. In this paper the problem of approximating LCS is studied, while focusing on the hard inputs for this problem, namely, approximating LCS of near-linear size in strings over relatively large alphabet (of size at least n ε for some constant ε> 0, where n is the length of the string). We show that, any given string over relatively large alphabet can be embedded into a local non-repetitive string. This embedding has a negligible additive distortion for strings that are not too dissimilar in terms of the edit distance. We also show that LCS can be efficiently approximated in locally-non-repetitive strings.

AB - A classical measure of similarity between strings is the length of the longest common subsequence(LCS) between the two given strings. The search for efficient algorithms for finding the LCS has been going on for more than three decades. To date, all known algorithms may take quadratic time (shaved by logarithmic factors) to find large LCS. In this paper the problem of approximating LCS is studied, while focusing on the hard inputs for this problem, namely, approximating LCS of near-linear size in strings over relatively large alphabet (of size at least n ε for some constant ε> 0, where n is the length of the string). We show that, any given string over relatively large alphabet can be embedded into a local non-repetitive string. This embedding has a negligible additive distortion for strings that are not too dissimilar in terms of the edit distance. We also show that LCS can be efficiently approximated in locally-non-repetitive strings.

UR - http://www.scopus.com/inward/record.url?scp=70350654581&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02441-2_9

DO - 10.1007/978-3-642-02441-2_9

M3 - Conference contribution

AN - SCOPUS:70350654581

SN - 3642024408

SN - 9783642024405

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

SP - 92

EP - 105

BT - Combinatorial Pattern Matching - 20th Annual Symposium, CPM 2009, Proceedings

T2 - 20th Annual Symposium on Combinatorial Pattern Matching, CPM 2009

Y2 - 22 June 2009 through 24 June 2009

ER -