Near-optimal algorithm to count occurrences of subsequences of a given length

Author:

Torres-Jimenez Jose1,Izquierdo-Marquez Idelfonso1,Ramirez-Acuna Daniel1,Peralta Rene2

Affiliation:

1. CINVESTAV-Tamaulipas, Information Technology Laboratory, Km. 5.5 Carretera Cd. Victoria-Soto la Marina, 87130, Cd. Victoria Tamps., México

2. National Institute of Standards and Technology, Gaithersburg, MD 20899-8910, USA

Abstract

For [Formula: see text], define [Formula: see text] as the set of integers [Formula: see text]. Given an integer [Formula: see text] and a string [Formula: see text] of length [Formula: see text] over [Formula: see text], we count the number of times that each one of the [Formula: see text] distinct strings of length [Formula: see text] over [Formula: see text] occurs as a subsequence of [Formula: see text]. Our algorithm makes only one scan of [Formula: see text] and solves the problem in time complexity [Formula: see text] and space complexity [Formula: see text]. These are very close to best possible.

Funder

Consejo Nacional de Ciencia y Tecnología

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

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