Improved algorithms for the range next value problem and applications

Authors:
Maxime Crochemore;Costas S. Iliopoulos;Marcin Kubica;M. Sohel Rahman;German Tischler;Tomasz Wale
Affiliations:
Algorithm Design Group, Department of Computer Science, Kings College London, Strand, London WC2R 2LS, England, United Kingdom and Institut Gaspard-Monge, Université de Marne-la-Vallée, ...;Algorithm Design Group, Department of Computer Science, Kings College London, Strand, London WC2R 2LS, England, United Kingdom;Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland;A EDA Group, Department of CSE, BUET, Dhaka-1000, Bangladesh;Lehrstuhl für Informatik II, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany;Institute of Informatics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

The Range Next Value problem (problem RNV) is a recent interesting variant of the range search problems, where the query is for the immediate next (or equal) value of a given number within a given interval of an array. Problem RNV was introduced and studied very recently by Crochemore et al. [Maxime Crochemore, Costas S. Iliopoulos, M. Sohel Rahman, Finding patterns in given intervals, in: Antonin Kucera, Ludek Kucera (Eds.), MFCS, 22 in: Lecture Notes in Computer Science, vol. 4708, Springer, 2007, pp. 645-656]. In this paper, we present improved algorithms for problem RNV and algorithms for extended versions of the RNV problem. We also show how this problem can be used to achieve optimal query time for a number of interesting variants of the classic pattern matching problems.