2021-10-27T01:51:57Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/470582017-10-15T15:00:00Zhdl_2115_20053hdl_2115_145Algorithms for Finding a Minimum Repetition Representation of a StringNakamura, AtsuyoshiSaito, TomoyaTakigawa, IchigakuMamitsuka, HiroshiKudo, Mineichitandem repeatstring algorithm007A string with many repetitions can be written compactly by replacing h-fold 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 CMR-C that is faster but can be applied only when the repetition weight function is constant. CMR-C 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, CMR-C is an O(n2 log n)-time O(n log n)-space algorithm, which is faster than CMR by ((log n)/n)-factor.String Processing and Information Retrieval (17th International Symposium, SPIRE 2010, Los Cabos, Mexico, October 11-13, 2010. Proceedings), ed. by Edgar Chavez; Stefano Lonardi, ISBN: 978-3-642-16320-3, (Lecture Notes in Computer Science; 6393/2010), pp. 185-190Springer Berlin / HeidelbergBookapplication/pdfhttp://hdl.handle.net/2115/47058https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/47058/3/LNCS6393_185-190.pdf2010enginfo:doi/10.1007/978-3-642-16321-0_18The original publication is available at www.springerlink.comauthor