Papers › TSP Escapes the O(2ⁿ n²) Curse
TSP Escapes the O(2ⁿ n²) Curse
Mihail Stoian
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The dynamic programming solution to the traveling salesman problem due to Bellman, and independently Held and Karp, runs in time O(2ⁿ n²), 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 2ⁿ n² / 2^(Ω(√(logn))). We achieve this by strategically remodeling the dynamic programming recursion as a min-plus matrix product, for which faster-than-na\"ive algorithms exist.
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