Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Information Science and Technology / Faculty of Information Science and Technology >
Peerreviewed Journal Articles, etc >
Algorithms for Finding a Minimum Repetition Representation of a String
Title:  Algorithms for Finding a Minimum Repetition Representation of a String 
Authors:  Nakamura, Atsuyoshi Browse this author →KAKEN DB  Saito, Tomoya Browse this author  Takigawa, Ichigaku Browse this author  Mamitsuka, Hiroshi Browse this author  Kudo, Mineichi Browse this author 
Keywords:  tandem repeat  string algorithm 
Issue Date:  2010 
Publisher:  Springer Berlin / Heidelberg 
Citation:  String Processing and Information Retrieval (17th International Symposium, SPIRE 2010, Los Cabos, Mexico, October 1113, 2010. Proceedings), ed. by Edgar Chavez; Stefano Lonardi, ISBN: 9783642163203, (Lecture Notes in Computer Science; 6393/2010), pp. 185190 
Publisher DOI:  10.1007/9783642163210_18 
Abstract:  A string with many repetitions can be written compactly by replacing hfold contiguous repetitions of substring r with (r)h. We refer to such a compact representation as a repetition representation string or RRS, by which a set of disjoint or nested tandem arrays can be compacted. In this paper, we study the problem of finding a minimum RRS or MRRS, where the size of an RRS is defined to be the sum of its component letter sizes and the sizes needed to describe the repetitions (・)h which are defined as wR(h) using a repetition weight function wR. We develop two dynamic programming algorithms to solve the problem. One is CMR that works for any repetition weight function, and the other is CMRC that is faster but can be applied only when the repetition weight function is constant. CMRC is an O(w(n + z))time algorithm using O(n + z) space for a given string with length n, where w and z are the number of distinct primitive tandem repeats and the number of their occurrences, respectively. Since w = O(n) and z = O(n log n) in the worst case, CMRC is an O(n2 log n)time O(n log n)space algorithm, which is faster than CMR by ((log n)/n)factor. 
Rights:  The original publication is available at www.springerlink.com 
Type:  bookchapter (author version) 
URI:  http://hdl.handle.net/2115/47058 
Appears in Collections:  情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peerreviewed Journal Articles, etc)

Submitter: 中村 篤祥
