New directions in sublinear algorithms and testing properties of distributions

This thesis deals with sublinear algorithms for various types of problems in statistics, combinatorial optimization and graph algorithms. A first focus of this thesis is algorithms for testing whether a probability distribution, to which the algorithms have sample access, is equal to a given hypothesis distribution, using a number of samples that is sublinear in the domain size. A second focus is to consider various other models of computation defined by type of queries available to the user. This thesis shows how more powerful queries, such as the ability to get a sample according to the conditional distribution on a specified set, allows one to get faster algorithms for a number of problems. Thirdly, this thesis considers the problem of certifying and correcting the result of a crowdsourced computation with potentially erroneous worker reports, by using verification queries on a sublinear number of reports. Finally, we show improved methods to simulate graph algorithms for maximal independent set, minimum vertex cover and maximum matching by distributing the computation to multiple sublinear space computing machines and allowing only a sublinear number of rounds of communication between them.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Gouleakis, Themistoklis

Advisor dc:contributor.advisor

• Ronitt Rubinfeld.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/120434

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/120434