Counting common substrings effectively

TL;DR

This paper introduces an efficient dynamic algorithm for counting common substrings between two strings, facilitating quick string similarity measurements using generalized n-gram methods like Niewiadomski's measure.

Contribution

The paper presents a novel dynamic algorithm for counting shared substrings, with proven correctness and complexity analysis, applicable to string similarity calculations.

Findings

Algorithm effectively counts common substrings.

Correctness and complexity are rigorously analyzed.

Applicable to generalized n-gram similarity measures.

Abstract

This article presents effective (dynamic) algorithm for solving a problem of counting the number of substrings of given string which are also substrings of second string. Presented algorithm can be used for example for quick calculation of strings similarity measure using generalized $n$-gram method (Niewiadomski measure), which are shown. Correctness and complexity analyses are included. ----- W artykule przedstawiono efektywny (dynamiczny) algorytm wyznaczaj\k{a}cy miar\k{e} podobie\'nstwa wyraz\'ow za pomoc\k{a} uog\'olnionej metody $n$-gram\'ow (miary Niewiadomskiego). Uzasadniono tak\.ze poprawno\'s\'c dzia{\l}ania algorytmu i oszacowano jego z{\l}o\.zono\'s\'c obliczeniow\k{a}.