Fine-grained complexity meets communication complexity

Fine-grained complexity aims to understand the exact exponent of the running time of fundamental problems in P. Basing on several important conjectures such as Strong Exponential Time Hypothesis (SETH), All-Pair Shortest Path Conjecture, and the 3-Sum Conjecture, tight conditional lower bounds are proved for numerous exact problems from all fields of computer science, showing that many text-book algorithms are in fact optimal. For many natural problems, a fast approximation algorithm would be as important as fast exact algorithms. So it would be interesting to show hardness for approximation algorithms as well. But we had few techniques to prove tight hardness for approximation problems in P--In particular, the celebrated PCP Theorem, which proves similar approximation hardness in the world of NP-completeness, is not fine-grained enough to yield interesting conditional lower bounds for approximation problems in P.

Name thesis:degree_name

Master

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

2019

Author dc:creator

• Chen, Lijie(Electrical and computer science engineer)Massachusetts Institute of Technology.

Advisor dc:contributor.advisor

• Richard R. Williams.

• 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

https://hdl.handle.net/1721.1/122754

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/122754