Skip to feedback

Award Abstract # 0829672
Invariance in Property Testing

NSF Org: CCF
Division of Computing and Communication Foundations
Recipient: MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Initial Amendment Date: July 18, 2008
Latest Amendment Date: August 18, 2009
Award Number: 0829672
Award Instrument: Continuing Grant
Program Manager: Dmitri Maslov
CCF
 Division of Computing and Communication Foundations
CSE
 Directorate for Computer and Information Science and Engineering
Start Date: September 1, 2008
End Date: August 31, 2013 (Estimated)
Total Intended Award Amount: $450,000.00
Total Awarded Amount to Date: $450,000.00
Funds Obligated to Date: FY 2008 = $300,000.00
FY 2009 = $150,000.00
History of Investigator:
  • Madhu Sudan (Principal Investigator)
    madhu@cs.harvard.edu
Recipient Sponsored Research Office: Massachusetts Institute of Technology
77 MASSACHUSETTS AVE
CAMBRIDGE
MA  US  02139-4301
(617)253-1000
Sponsor Congressional District: 07
Primary Place of Performance: Massachusetts Institute of Technology
77 MASSACHUSETTS AVE
CAMBRIDGE
MA  US  02139-4301
Primary Place of Performance
Congressional District:
07
Unique Entity Identifier (UEI): E2NYLCDML6V1
Parent UEI: E2NYLCDML6V1
NSF Program(s): Information Technology Researc,
THEORY OF COMPUTING,
Special Projects - CCF
Primary Program Source: 01000809DB NSF RESEARCH & RELATED ACTIVIT
01000910DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 9218, HPCC
Program Element Code(s): 164000, 286000, 287800
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.070

ABSTRACT

This project initiates new, unifying directions in Property Testing.
Property Testing is the area of algorithmic research that attempts to discover global properties of data by by sampling the data probabilistically in very few places. The ``oldest'' property test might be the use of polling to predict the outcome of an upcoming election. Modern research has extended the scope of property tests to a much richer class of properties including tests of linearity (``is the data essentially linear with respect to some parameters"), multilinearity, low-degreeness, colorability (``is the data describing a graph with small chromatic number") etc.

The goal of this project is to shed light on the question: What makes some properties testable so efficiently, that we do not have to look at the entire data in order to test for it? The thesis underlying the project is that for interesting properties, testability ought to be related to the ``invariances" shown by the property: i.e., if the data is viewed as a function from some input to some output, then the ``invariances" are given by a set (a group) of permutations of the input space under which the property remains unchanged. The project explores a variety of potential invariances to consider and studies conditions under which {\em every} property exhibiting such invariance is testable.

The broader impact of the project is to find ways of coping with the data explosion problem faced by many computers, by describing settings where massive data may be analyzed by sampling small pieces.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

Note:  When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

(Showing: 1 - 10 of 13)
Arnab Bhattacharyya, Victor Chen, Madhu Sudan, and Ning Xie "Testing Linear-Invariant Non-Linear Properties" Theory of Computing , v.7(1) , 2011 , p.75-99
Elad Haramaty, Amir Shpilka, and Madhu Sudan "Optimal Testing of Multivariate Polynomials over Small Prime Fields" SIAM Journal on Computing , v.42 , 2013 , p.536-562
Elena Grigorescu, Tali Kaufman, and Madhu Sudan "2-Transitivity is Insufficient for Local Testability" Computational Complexity , v.22 , 2013 , p.137-158
Elena Grigorescu, Tali Kaufman, and Madhu Sudan "Succinct Representation of Codes with Applications to Testing" SIAM Journal of Discrete Math , v.26 , 2012 , p.1618-1634
Eli Ben-Sasson, Venkatesan Guruswami, Tali Kaufman, Madhu Sudan, and Michael Viderman "Locally Testable Codes Require Redundant Testers" SIAM Journal on Computing , v.39(7) , 2010 , p.3230-3247
Gagan Aggarwal, Amos Fiat, Andrew Goldberg, Jason Hartline, Nicole Immorlica, and Madhu Sudan "Derandomization of Auctions" Games and Economic Behavior , v.7(1) , 2011 , p.1-11
Madhu Sudan "Guest column: Testing Linear Properties: Some General Themes" SIGACT News , v.42(1) , 2011 , p.59-80
Madhu Sudan "Patterns hidden from simple algorithms, Technical Perspective" Communications of the ACM , v.54(4) , 2011 , p.107
Madhu Sudan "Probabilistically Checkable Proofs" Communications of the ACM , v.52(3) , 2009 , p.76-84
Shubhangi Saraf "Acute and nonobtuse triangulations of polyhedral surfaces" European Journal of Combinatorics , v.30(4) , 2009 , p.833-840
Shubhangi Saraf and Madhu Sudan "An improved lower bound on the size of Kakeya sets over finite fields" Analysis & PDE , v.1(3) , 2008 , p.375-379
(Showing: 1 - 10 of 13)

Please report errors in award information by writing to: awardsearch@nsf.gov.

Print this page

Back to Top of page