Tight Hardness Results for LCS and Other Sequence Similarity Measures

Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of applications. Simple dynamic programming algorithms solve these task...

Full description

Saved in:
Bibliographic Details
Published in2015 IEEE 56th Annual Symposium on Foundations of Computer Science pp. 59 - 78
Main Authors Abboud, Amir, Backurs, Arturs, Williams, Virginia Vassilevska
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.10.2015
Subjects
Biology
Complexity theory
Computer science
Cost function
DTWD
Dynamic programming
Heuristic algorithms
LCS
lower bounds
parameterized complexity
sequence alignments
SETH
Time measurement
Online AccessGet full text
ISSN0272-5428
DOI10.1109/FOCS.2015.14

Cover

More Information
Summary:Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of applications. Simple dynamic programming algorithms solve these tasks in O(n 2 ) time, and despite an extensive amount of research, no algorithms with significantly better worst case upper bounds are known. In this paper, we show that for any constant ε >0, an O(n 2-ε ) time algorithm for computing the LCS or the DTWD of two sequences of length n over a constant size alphabet, refutes the popular Strong Exponential Time Hypothesis (SETH).
ISSN:0272-5428
DOI:10.1109/FOCS.2015.14