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

Ferdinando Cicalese, Eduardo Laber, Oren Weimann, Raphael Yuster

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 23rd Annual Symposium, CPM 2012, Proceedings
Pages149-158
Number of pages10
DOIs
StatePublished - 2012
Event23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012 - Helsinki, Finland
Duration: 3 Jul 20125 Jul 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7354 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012
Country/TerritoryFinland
CityHelsinki
Period3/07/125/07/12

Keywords

  • Parikh vectors
  • approximate pattern matching
  • approximation algorithms
  • maximum subsequence sum

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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