4 research outputs found
Fast and Simple Jumbled Indexing for Binary Run-Length Encoded Strings
Important papers have appeared recently on the problem of indexing binary strings for jumbled pattern matching, and further lowering the time bounds in terms of the input size would now be a breakthrough with broad implications. We can still make progress on the problem, however, by considering other natural parameters. Badkobeh et al. (IPL, 2013) and Amir et al. (TCS, 2016) gave algorithms that index a binary string in O(n + r^2 log r) time, where n is the length and r is the number of runs, and Giaquinta and Grabowski (IPL, 2013) gave one that runs in O(n + r^2) time. In this paper we propose a new and very simple algorithm that also runs in O(n + r^2) time and can be extended either so that the index returns the position of a match (if there is one), or so that the algorithm uses only O(n) bits of space instead of O(n) words
Fast and Simple Jumbled Indexing for Binary Run-Length Encoded Strings
Cunha L, Dantas S, Gagie T, Wittler R, Kowada L, Stoye J. Fast and Simple Jumbled Indexing for Binary Run-Length Encoded Strings. In: Proceedings of CPM 2017. LIPIcs. Vol 78. 2017: 19:1-19:9
On Infinite Prefix Normal Words
Prefix normal words are binary words that have no factor with more s than
the prefix of the same length. Finite prefix normal words were introduced in
[Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal
words and explore their relationship to some known classes of infinite binary
words. In particular, we establish a connection between prefix normal words and
Sturmian words, between prefix normal words and abelian complexity, and between
prefix normality and lexicographic order.Comment: 20 pages, 4 figures, accepted at SOFSEM 2019 (45th International
Conference on Current Trends in Theory and Practice of Computer Science,
Nov\'y Smokovec, Slovakia, January 27-30, 2019