TY - GEN

T1 - Weighted ancestors in suffix trees

AU - Gawrychowski, Paweł

AU - Lewenstein, Moshe

AU - Nicholson, Patrick K.

PY - 2014

Y1 - 2014

N2 - The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalisation to weighted trees, a.k.a. the weighted ancestor problem, has been extensively explored and successfully reduced to the predecessor problem. It is known that any data structure solution for the weighted ancestor problem that occupies O(n polylog(n)) space must have Ω(loglogn) query time, if the weights are drawn from a polynomially bounded universe. Perhaps the most important and frequent application of the weighted ancestors problem is for suffix trees. It has been a long-standing open question whether the weighted ancestors problem has better bounds for suffix trees. We answer this question positively: we show that a suffix tree built for a text w[1.n] can be preprocessed using O(n) extra space, so that queries can be answered in O(1) time. Thus we improve the running times of several applications. Our improvement is based on a number of data structure tools and a periodicity-based insight into the combinatorial structure of a suffix tree.

AB - The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalisation to weighted trees, a.k.a. the weighted ancestor problem, has been extensively explored and successfully reduced to the predecessor problem. It is known that any data structure solution for the weighted ancestor problem that occupies O(n polylog(n)) space must have Ω(loglogn) query time, if the weights are drawn from a polynomially bounded universe. Perhaps the most important and frequent application of the weighted ancestors problem is for suffix trees. It has been a long-standing open question whether the weighted ancestors problem has better bounds for suffix trees. We answer this question positively: we show that a suffix tree built for a text w[1.n] can be preprocessed using O(n) extra space, so that queries can be answered in O(1) time. Thus we improve the running times of several applications. Our improvement is based on a number of data structure tools and a periodicity-based insight into the combinatorial structure of a suffix tree.

UR - http://www.scopus.com/inward/record.url?scp=84958532053&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-44777-2_38

DO - 10.1007/978-3-662-44777-2_38

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AN - SCOPUS:84958532053

SN - 9783662447765

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

SP - 455

EP - 466

BT - Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings

PB - Springer Verlag

T2 - 22nd Annual European Symposium on Algorithms, ESA 2014

Y2 - 8 September 2014 through 10 September 2014

ER -