TY - GEN

T1 - Range non-overlapping indexing and successive list indexing

AU - Keller, Orgad

AU - Kopelowitz, Tsvi

AU - Lewenstein, Moshe

PY - 2007

Y1 - 2007

N2 - We present two natural variants of the indexing problem: In the range non-overlapping indexing problem, we preprocess a given text to answer queries in which we are given a pattern, and wish to find a maximal-length 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 non-overlapping 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 query-time 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 indexing-related context.

AB - We present two natural variants of the indexing problem: In the range non-overlapping indexing problem, we preprocess a given text to answer queries in which we are given a pattern, and wish to find a maximal-length 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 non-overlapping 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 query-time 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 indexing-related context.

UR - http://www.scopus.com/inward/record.url?scp=38149120507&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-73951-7_54

DO - 10.1007/978-3-540-73951-7_54

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AN - SCOPUS:38149120507

SN - 3540739483

SN - 9783540739487

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 625

EP - 636

BT - Algorithms and Data Structures - 10th International Workshop, WADS 2007, Proceedings

PB - Springer Verlag

T2 - 10th International Workshop on Algorithms and Data Structures, WADS 2007

Y2 - 15 August 2007 through 17 August 2007

ER -