Language Edit Distance, (min,+)-Matrix Multiplication and Beyond

Saha, Barna

Title:

Language Edit Distance, (min,+)-Matrix Multiplication and Beyond

dc.contributor.author	Saha, Barna
dc.contributor.corporatename	Georgia Institute of Technology. Algorithms, Randomness and Complexity Center	en_US
dc.contributor.corporatename	University of Massachusetts at Amherst. College of Information and Computer Sciences	en_US
dc.date.accessioned	2017-10-31T17:25:09Z
dc.date.available	2017-10-31T17:25:09Z
dc.date.issued	2017-10-23
dc.description	Presented on October 23, 2017 at 11:00 a.m. in the Klaus Advanced Computing Building, Room 1116E.	en_US
dc.description	Barna Saha received her Ph.D. from the University of Maryland College Park, and then spent a couple of years at the AT&T Shannon Labs as a senior researcher before joining UMass Amherst in 2014. Her research interests are in theoretical computer science specifically in algorithm design and analysis, and large scale data analytics.	en_US
dc.description	Runtime: 56:58 minutes	en_US
dc.description.abstract	The language edit distance is a significant generalization of two basic problems in computer science: parsing and string edit distance computation. Given any context free grammar, it computes the minimum number of insertions, deletions and substitutions required to convert a given input string into a valid member of the language. In 1972, Aho and Peterson gave a dynamic programming algorithm that solves this problem in time cubic in the string length. Despite its vast number of applications, in forty years there has been no improvement over this running time. Computing (min,+)-product of two n by n matrices in truly subcubic time is an outstanding open question, as it is equivalent to the famous All-Pairs-Shortest-Paths problem. Even when matrices have entries bounded in [1,n], obtaining a truly subcubic (min,+)-product algorithm will be a major breakthrough in computer science. In this presentation, I will explore the connection between these two problems which led us to develop the first truly subcubic algorithms for the following problems with improvements coming for each of these problems after several decades: (1) language edit distance, (2) RNA-folding-a basic computational biology problem and a special case of language edit distance computation, (3) stochastic grammar parsing—fundamental to natural language processing, and (4) (min,+)-product of integer matrices with entries bounded in n^(3-ω-c) where c >0 is any constant and, ω is the exponent of the fast matrix multiplication, believed to be 2.	en_US
dc.format.extent	56:58 minutes
dc.identifier.uri	http://hdl.handle.net/1853/58857
dc.language.iso	en_US	en_US
dc.relation.ispartofseries	Algorithms and Randomness Center (ARC) Colloquium
dc.subject	Approximation algorithms	en_US
dc.subject	Fine-grained complexity	en_US
dc.subject	Matrix multiplication	en_US
dc.title	Language Edit Distance, (min,+)-Matrix Multiplication and Beyond	en_US
dc.type	Moving Image
dc.type.genre	Lecture
dspace.entity.type	Publication
local.contributor.corporatename	Algorithms and Randomness Center
local.contributor.corporatename	College of Computing
local.relation.ispartofseries	ARC Colloquium
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