Dynamic Programming meets Fine-grained Complexity

Since the term was coined by Richard Bellman in the 1940s, Dynamic Programming (DP) has remained one of the most popular technique in theoretical computer science, and has found applications in a wide range of problems. In this thesis, I summarize my three recent works covering applications of DP to three fundamental problems in fine-grained complexity. The first application is a sub-cubic time algorithm for unweighted tree edit distance (TED), the second application is an improved FPTAS (Fully Polynomial-Time Approximation Scheme) for Partition, and the third application is an improved FPTAS for Knapsack.

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

2022

Author dc:creator

• Mao, Xiao

Advisor dc:contributor.advisor

• Williams, Virginia Vassilevska

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/147497

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/147497