Fast computation of a longest increasing subsequence and application

Maxime Crochemore; Ely Porat

doi:10.1016/j.ic.2010.04.003

Fast computation of a longest increasing subsequence and application

Maxime Crochemore, Ely Porat

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

We consider the complexity of computing a longest increasing subsequence (LIS) parameterised by the length of the output. Namely, we show that the maximal length k of an increasing subsequence of a permutation of the set of integers {1,2,...,n} can be computed in time O(nloglogk) in the RAM model, improving the previous 30-year bound of O(nlogk). The algorithm also improves on the previous O(nloglogn) bound. The optimality of the new bound is an open question. Reducing the computation of a longest common subsequence (LCS) between two strings to an LIS computation leads to a simple O(rloglogk)-time algorithm for two sequences having r pairs of matching symbols and an LCS of length k.

Original language	English
Pages (from-to)	1054-1059
Number of pages	6
Journal	Information and Computation
Volume	208
Issue number	9
DOIs	https://doi.org/10.1016/j.ic.2010.04.003
State	Published - Sep 2010

Bibliographical note

Funding Information:
< Work partially supported by the Royal Society, UK. A preliminary version of the article has been presented at the conference “Visions of Computer Science”,

Funding

< Work partially supported by the Royal Society, UK. A preliminary version of the article has been presented at the conference “Visions of Computer Science”,

Funders	Funder number
Royal Society

Keywords

Data structures
Design and analysis of algorithms
Dynamic programming
Longest common subsequence
Longest increasing subsequence
Priority queue

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10.1016/j.ic.2010.04.003

Cite this

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Fast computation of a longest increasing subsequence and application

Abstract

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Keywords

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