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What and Who
Title:The (multivariate) fine-grained complexity of Longest Common Subsequence
Speaker:Marvin Künnemann
coming from:Max-Planck-Institut für Informatik - D1
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, D2, D3, D4, D5, RG1, SWS, MMCI
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Level:AG Audience
Language:English
Date, Time and Location
Date:Thursday, 25 February 2016
Time:13:00
Duration:30 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
Despite much effort, for the classic problem of finding a longest common subsequence (LCS) of strings x and y over an alphabet \Sigma, no algorithm with a worst-case running time of O((|x| \cdot |y|)^{1-\eps}) for any constant \eps > 0 is known. Recent work indeed shows that finding such an algorithm is impossible without refuting the Strong Exponential Time Hypothesis (SETH) [Abboud, Backurs, Vassilevska-Williams FOCS'15; Bringmann, K\"unnemann FOCS'15].

Notwithstanding the lack of improvement in the worst case, a long and successful line of research identified and exploited parameters of the input strings, achieving strongly subquadratic running times for highly relevant special cases, e.g., comparing large, but very similar files. The questions arise whether (i) the best known algorithms have an optimal parameter dependence (up to lower order factors, assuming SETH) and whether (ii) some parameter constellations admit faster algorithms than currently known (without refuting SETH). To this end, we provide a \emph{systematic}, effectively tight study of the (conditional) complexity of LCS, taking into account the parameters previously discussed in the literature: n:=max{|x|,|y|}, m:=min{|x|,|y|}, the length L of an LCS of x and y, the alphabet size |\Sigma|, m-L, n-L, as well as the numbers of matching and dominant pairs.

This is joint work with Karl Bringmann.

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Name(s):Marvin Künnemann
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Created by:Marvin Künnemann, 01/20/2016 01:28 PMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Marvin Künnemann, 01/20/2016 01:28 PM -- Created document.