On approximating projection games
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Cataloged from student-s...
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ndltd-MIT-oai-dspace.mit.edu-1721.1-1006352019-05-02T15:42:06Z On approximating projection games Manurangsi, Pasin Dana Moshkovitz. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015. 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 99-105). The projection games problem (also known as LABEL COVER) is a problem of great significance in the field of hardness of approximation since almost all NP-hardness of approximation results known today are derived from the NP-hardness of approximation of projection games. Hence, it is important to determine the exact approximation ratio at which projection games become NP-hard to approximate. The goal of this thesis is to make progress towards this problem. First and foremost, we present a polynomial-time approximation algorithm for satisfiable projection games, which achieves an approximation ratio that is better than that of the previously best known algorithm. On the hardness of approximation side, while we do not have any improved NP-hardness result of approximating LABEL COVER, we show a polynomial integrality gap for polynomially many rounds of the Lasserre SDP relaxation for projection games. This result indicates that LABEL COVER might indeed be hard to approximate to within some polynomial factor. In addition, we explore special cases of projection games where the underlying graphs belong to certain families of graphs. For planar graphs, we present both a subexponential-time exact algorithm and a polynomial-time approximation scheme (PTAS) for projection games. We also prove that these algorithms have tight running times. For dense graphs, we present a subexponential-time approximation algorithm for LABEL COVER. Moreover, if the graph is a sufficiently dense random graph, we show that projection games are easy to approximate to within any polynomial ratio. by Pasin Manurangsi. M. Eng. 2016-01-04T20:00:48Z 2016-01-04T20:00:48Z 2015 2015 Thesis http://hdl.handle.net/1721.1/100635 933231949 eng 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. http://dspace.mit.edu/handle/1721.1/7582 137 pages application/pdf Massachusetts Institute of Technology |
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Electrical Engineering and Computer Science. Manurangsi, Pasin On approximating projection games |
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Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015. === 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 99-105). === The projection games problem (also known as LABEL COVER) is a problem of great significance in the field of hardness of approximation since almost all NP-hardness of approximation results known today are derived from the NP-hardness of approximation of projection games. Hence, it is important to determine the exact approximation ratio at which projection games become NP-hard to approximate. The goal of this thesis is to make progress towards this problem. First and foremost, we present a polynomial-time approximation algorithm for satisfiable projection games, which achieves an approximation ratio that is better than that of the previously best known algorithm. On the hardness of approximation side, while we do not have any improved NP-hardness result of approximating LABEL COVER, we show a polynomial integrality gap for polynomially many rounds of the Lasserre SDP relaxation for projection games. This result indicates that LABEL COVER might indeed be hard to approximate to within some polynomial factor. In addition, we explore special cases of projection games where the underlying graphs belong to certain families of graphs. For planar graphs, we present both a subexponential-time exact algorithm and a polynomial-time approximation scheme (PTAS) for projection games. We also prove that these algorithms have tight running times. For dense graphs, we present a subexponential-time approximation algorithm for LABEL COVER. Moreover, if the graph is a sufficiently dense random graph, we show that projection games are easy to approximate to within any polynomial ratio. === by Pasin Manurangsi. === M. Eng. |
author2 |
Dana Moshkovitz. |
author_facet |
Dana Moshkovitz. Manurangsi, Pasin |
author |
Manurangsi, Pasin |
author_sort |
Manurangsi, Pasin |
title |
On approximating projection games |
title_short |
On approximating projection games |
title_full |
On approximating projection games |
title_fullStr |
On approximating projection games |
title_full_unstemmed |
On approximating projection games |
title_sort |
on approximating projection games |
publisher |
Massachusetts Institute of Technology |
publishDate |
2016 |
url |
http://hdl.handle.net/1721.1/100635 |
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AT manurangsipasin onapproximatingprojectiongames |
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