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T.: Improved algorithms for the range next value problem and applications
 In: Proc. STACS
, 2008
"... 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. ..."
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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 [Finding Patterns In Given Intervals, MFCS 2007]. In this paper, we present improved algorithms for Problem RNV. 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. 1.
Range nonoverlapping indexing and successive list indexing
 of Lecture Notes in Computer Science
, 2007
"... Abstract. We present two natural variants of the indexing problem: In the range nonoverlapping indexing problem, we preprocess a given text to answer queries in which we are given a pattern, and wish to find a maximallength sequence of occurrences of the pattern in the text, such that the occurren ..."
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Cited by 5 (0 self)
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Abstract. We present two natural variants of the indexing problem: In the range nonoverlapping indexing problem, we preprocess a given text to answer queries in which we are given a pattern, and wish to find a maximallength sequence of occurrences of the pattern in the text, such that the occurrences do not overlap with one another. While efficiently solving this problem, our algorithm even enables us to efficiently perform so in substrings of the text, denoted by given start and end locations. The methods we supply thus generalize the string statistics problem [4, 5], in which we are asked to report merely the number of nonoverlapping occurrences in the entire text, by reporting the occurrences themselves, even only for substrings of the text. In the related successive list indexing problem, during querytime we are given a pattern and a list of locations in the preprocessed text. We then wish to find a list of occurrences of the pattern, such that the ith occurrence is the leftmost occurrence of the pattern which starts to the right of the ith location given by the input list. Both problems are solved by using tools from computational geometry, specifically a variation of the range searching for minimum problem of Lenhof and Smid [12], here considered over a grid, in what appears to be the first utilization of range searching for minimum in an indexingrelated context. 1
On the Number of Maximal Bipartite Subgraphs of a Graph, BRICS
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Cited by 1 (0 self)
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
www.stacsconf.org IMPROVED ALGORITHMS FOR THE RANGE NEXT VALUE PROBLEM AND APPLICATIONS
"... 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. ..."
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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 [Finding Patterns In Given Intervals, MFCS 2007]. In this paper, we present improved algorithms for Problem RNV. 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. 1.
Barcelona Aarhus Barcelona
, 2002
"... This is the second annual progress report for the ALCOMFT project, supported by the European ..."
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This is the second annual progress report for the ALCOMFT project, supported by the European
ASK NOT WHAT STRINGOLOGY CAN DO FOR YOU: ADVANCES IN PATTERN MATCHING DRIVEN BY COMPUTATIONAL
"... Abstract. Molecular biology has posed a number of fascinating and sometimes daunting computational problems, which came naturally expressed in its native language of character strings. Through the years, some such problems have found elegant and even useful solutions in response to the needs that or ..."
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Abstract. Molecular biology has posed a number of fascinating and sometimes daunting computational problems, which came naturally expressed in its native language of character strings. Through the years, some such problems have found elegant and even useful solutions in response to the needs that originally motivated them. What is perhaps even more remarkable, several of the ideas inspired by computational molecular biology have found application in remote and diverse domains, so that it may be argued that molecular biology did more for computing than the latter did for it. As a modest tribute, this paper reviews a small sample of these cases drawing from the personal exposure of the author.
Range NonOverlapping Indexing
, 909
"... Abstract. We study the nonoverlapping indexing problem: Given a text T, preprocess it in order to answer queries of the form: given a pattern P, report the maximal set of nonoverlapping occurrences of P in T. A generalization of this problem is the range nonoverlapping indexing where in addition ..."
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Abstract. We study the nonoverlapping indexing problem: Given a text T, preprocess it in order to answer queries of the form: given a pattern P, report the maximal set of nonoverlapping occurrences of P in T. A generalization of this problem is the range nonoverlapping indexing where in addition we are given two indexes i, j to report the maximal set of nonoverlapping occurrences between these two indexes. We suggest new solutions for these problems. For the nonoverlapping problem our solution uses O(n) space with query time of O(m+occNO). For the range nonoverlapping problem we propose a solution with O(n log ǫ n) space for some 0 < ǫ < 1 and O(m + log log n + occij,NO) query time. 1 Introduction and Related Work Given a text T of length n over an alphabet Σ, the text indexing problem is to build an index on T which can answer pattern matching queries efficiently: Given a pattern P of length m, we want to report all its occurrences in T. There are some known solutions for this problem. For instance, the suffix tree, proposed by
a Grupo de Procesamiento de Lenguaje Natural
, 2012
"... Motivated by the inference of the structure of genomic sequences, we address here the smallest grammar problem. In previous work, we introduced a new perspective on this problem, splitting the task into two different optimization problems: choosing which words will be considered constituents of the ..."
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Motivated by the inference of the structure of genomic sequences, we address here the smallest grammar problem. In previous work, we introduced a new perspective on this problem, splitting the task into two different optimization problems: choosing which words will be considered constituents of the final grammar and finding a minimal parsing with these constituents. Here we focus on making these ideas applicable on large sequences. First, we improve the complexity of existing algorithms by using the concept of maximal repeats when choosing which substrings will be the constituents of the grammar. Then, we improve the size of the grammars by cautiously adding a minimal parsing optimization step. Together, these approaches enable us to propose new practical algorithms that return smaller grammars (up to 10%) in approximately the same amount of time than their competitors on a classical set of genomic sequences and on whole genomes of model organisms.