research-article

AnO(ND) difference algorithm and its variations

Author:

Eugene W. MyersAuthors Info & Claims

Algorithmica, Volume 1, Issue 1-4

Pages 251 - 266

https://doi.org/10.1007/BF01840446

Published: 22 March 2023 Publication History

Abstract

The problems of finding a longest common subsequence of two sequencesA andB and a shortest edit script for transformingA intoB have long been known to be dual problems. In this paper, they are shown to be equivalent to finding a shortest/longest path in an edit graph. Using this perspective, a simpleO(ND) time and space algorithm is developed whereN is the sum of the lengths ofA andB andD is the size of the minimum edit script forA andB. The algorithm performs well when differences are small (sequences are similar) and is consequently fast in typical applications. The algorithm is shown to haveO(N+D²) expected-time performance under a basic stochastic model. A refinement of the algorithm requires onlyO(N) space, and the use of suffix trees leads to anO(N logN+D²) time variation.

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Published In

cover image Algorithmica

Algorithmica Volume 1, Issue 1-4

Nov 1986

517 pages

ISSN:0178-4617

Issue’s Table of Contents

© Springer-Verlag New York Inc. 1986.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 22 March 2023

Revision received: 17 January 1986

Received: 11 June 1985

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