References & Citations
Computer Science > Data Structures and Algorithms
Title: TSP Escapes the $O(2^n n^2)$ Curse
(Submitted on 5 May 2024)
Abstract: The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time $O(2^n n^2)$, with no improvement in the last sixty years. We break this barrier for the first time by designing an algorithm that runs in deterministic time $2^n n^2 / 2^{\Omega(\sqrt{\log n})}$. We achieve this by strategically remodeling the dynamic programming recursion as a min-plus matrix product, for which faster-than-na\"ive algorithms exist.
Link back to: arXiv, form interface, contact.