Dynamic Programming meets Fine-grained Complexity

Abstract

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.