Computing a longest increasing subsequence of length k in time O(n log log k)

Authors:
MAXIME CROCHEMORE;ELY PORAT
Affiliations:
King's College London, Strand, London, UK and Université Paris-Est.;Bar-Ilan University, Ramat-Gan, Israel
Venue:
VoCS'08 Proceedings of the 2008 international conference on Visions of Computer Science: BCS International Academic Conference
Year:
2008

Citing 6
Cited 1

A fast algorithm for computing longest common subsequences

Communications of the ACM
Enumerating longest increasing subsequences and patience sorting

Information Processing Letters
A Subquadratic Sequence Alignment Algorithm for Unrestricted Scoring Matrices

SIAM Journal on Computing
Deterministic sorting in O(nlog logn) time and linear space

Journal of Algorithms
Data streams: algorithms and applications

Foundations and Trends® in Theoretical Computer Science
A fast algorithm for computing a longest common increasing subsequence

Information Processing Letters

LCS Approximation via Embedding into Local Non-repetitive Strings

CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the complexity of computing a longest increasing subsequence 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(n log log k) in the RAM model, improving the previous 30-year bound of O(n log log k). The optimality of the new bound is an open question.