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 -