## 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 of Parikh vectors in a bit string. Recently, several attempts have been made to build indexes for all Parikh vectors of a binary string in subquadratic time. However, no algorithm is known to date which can beat by more than a polylogarithmic factor the naive Θ(n^{2}) procedure. We show how to construct a (1+ε)-approximate index for all Parikh vectors of a binary string in O(n^{log2n}/log(1+ε)) time, for any constant ε>0. Such index is approximate, in the sense that it leaves a small chance for false positives (no false negatives are 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 subquadratic running time.

Original language | English |
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Pages (from-to) | 130-137 |

Number of pages | 8 |

Journal | Theoretical Computer Science |

Volume | 525 |

DOIs | |

State | Published - 13 Mar 2014 |

## Keywords

- Approximate pattern matching
- Maximum subsequence sum
- Parikh vectors
- Permutation pattern matching

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science