Advanced Search

Deterministic network coding by matrix completion

Research and Teaching Output of the MIT Community

Show simple item record

dc.contributor.advisor David R. Karger. en_US Harvey, Nicholas James Alexander en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US 2006-09-28T15:03:27Z 2006-09-28T15:03:27Z 2005 en_US 2005 en_US
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005. en_US
dc.description Includes bibliographical references (leaves 81-85). en_US
dc.description.abstract Network coding is a new field of research that addresses problems of transmitting data through networks. Multicast problems are an important class of network coding problems where there is a single sender and all data must be transmitted to a set of receivers. In this thesis, we present a new deterministic algorithm to construct solutions for multicast problems that transmit data at the maximum possible rate. Our algorithm easily generalizes to several variants of multicast problems. Our approach is based on a new algorithm for maximum-rank completion of mixed matrices-taking a matrix whose entries are a mixture of numeric values and symbolic variables, and assigning values to the variables so as to maximize the resulting matrix rank. Our algorithm is faster than existing deterministic algorithms and can operate over smaller fields. This algorithm is extended to handle collections of matrices that can share variables. Over sufficiently large fields, the algorithm can compute a completion that simultaneously maximizes the rank of all matrices in the collection. Our simultaneous matrix completion algorithm requires working over a field whose size exceeds the number of matrices in the collection. We show that this algorithm is best-possible, in the sense that no efficient algorithm can operate over a smaller field unless P=NP. en_US
dc.description.statementofresponsibility by Nicholas James Alexander Harvey. en_US
dc.format.extent 85 leaves en_US
dc.format.extent 4702338 bytes
dc.format.extent 4705809 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.subject Electrical Engineering and Computer Science. en_US
dc.title Deterministic network coding by matrix completion en_US
dc.type Thesis en_US S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. en_US
dc.identifier.oclc 67616867 en_US

Files in this item

Name Size Format Description
67616867-MIT.pdf 3.843Mb PDF Full printable version

This item appears in the following Collection(s)

Show simple item record