Below P vs NP : fine-grained hardness for big data problems
Name
1084284848-MIT.pdf
Description
Full printable version
Size
1.16 MB
Format
Adobe PDF
Checksum (MD5)
3b0af62a4f739f961588a14664caf28c
Author(s)
Backurs, Arturs
Advisor(s)
Piotr Indyk.
Alternative Title
Fine-grained hardness for big data problems
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
The theory of NP-hardness has been remarkably successful in identifying problems that are unlikely to be solvable in polynomial time. However, many other important problems do have polynomial-time algorithms, but large exponents in their runtime bounds can make them inefficient in practice. For example, quadratic-time algorithms, although practical on moderately sized inputs, can become inefficient on big data problems that involve gigabytes or more of data. Although for many data analysis problems no sub-quadratic time algorithms are known, any evidence of quadratic-time hardness has remained elusive. In this thesis we present hardness results for several text analysis and machine learning tasks: ** Lower bounds for edit distance, regular expression matching and other pattern matching and string processing problems. ** Lower bounds for empirical risk minimization such as kernel support vectors machines and other kernel machine learning problems. All of these problems have polynomial time algorithms, but despite extensive amount of research, no near-linear time algorithms have been found. We show that, under a natural complexity-theoretic conjecture, such algorithms do not exist. We also show how these lower bounds have inspired the development of efficient algorithms for some variants of these problems.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 145-156).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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