TY - GEN

T1 - Near linear time construction of an approximate index for all maximum consecutive sub-sums of a sequence

AU - Cicalese, Ferdinando

AU - Laber, Eduardo

AU - Weimann, Oren

AU - Yuster, Raphael

PY - 2012

Y1 - 2012

N2 - We present a novel approach for computing all maximum consecutive subsums in a sequence of positive integers in near linear time. Solutions for this problem over binary sequences can be used for reporting existence (and possibly one occurrence) of Parikh vectors in a bit string. Recently, several attempts have been tried to build indexes for all Parikh vectors of a binary string in subquadratic time. However, to the best of our knowledge, no algorithm is know to date which can beat by more than a polylogarithmic factor the natural Θ(n 2) exhaustive procedure. Our result implies an approximate construction of an index for all Parikh vectors of a binary string in O(n 1 + η ) time, for any constant η > 0. Such index is approximate, in the sense that it leaves a small chance for false positives, i.e., Parikh vectors might be reported which are not actually present in the string. No false negative is possible. However, we can tune the parameters of the algorithm so that we can strictly control such a chance of error while still guaranteeing strong sub-quadratic running time.

AB - We present a novel approach for computing all maximum consecutive subsums in a sequence of positive integers in near linear time. Solutions for this problem over binary sequences can be used for reporting existence (and possibly one occurrence) of Parikh vectors in a bit string. Recently, several attempts have been tried to build indexes for all Parikh vectors of a binary string in subquadratic time. However, to the best of our knowledge, no algorithm is know to date which can beat by more than a polylogarithmic factor the natural Θ(n 2) exhaustive procedure. Our result implies an approximate construction of an index for all Parikh vectors of a binary string in O(n 1 + η ) time, for any constant η > 0. Such index is approximate, in the sense that it leaves a small chance for false positives, i.e., Parikh vectors might be reported which are not actually present in the string. No false negative is possible. However, we can tune the parameters of the algorithm so that we can strictly control such a chance of error while still guaranteeing strong sub-quadratic running time.

KW - Parikh vectors

KW - approximate pattern matching

KW - approximation algorithms

KW - maximum subsequence sum

UR - http://www.scopus.com/inward/record.url?scp=84863084387&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31265-6_12

DO - 10.1007/978-3-642-31265-6_12

M3 - Conference contribution

AN - SCOPUS:84863084387

SN - 9783642312649

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

SP - 149

EP - 158

BT - Combinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings

T2 - 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012

Y2 - 3 July 2012 through 5 July 2012

ER -