# Determinant Sums for Undirected Hamiltonicity

@article{Bjrklund2014DeterminantSF, title={Determinant Sums for Undirected Hamiltonicity}, author={Andreas Bj{\"o}rklund}, journal={SIAM J. Comput.}, year={2014}, volume={43}, pages={280-299} }

We present a Monte Carlo algorithm for Hamiltonicity detection in an $n$-vertex undirected graph running in $O(1.657^{n})$ time. To the best of our knowledge, this is the first superpolynomial improvement on the worst case runtime for the problem since the $O^*(2^n)$ bound established for the traveling salesman problem (TSP) over 50 years ago [R. Bellman, J. Assoc. Comput. Mach., 9 (1962), pp. 61--63], [M. Held and R. M. Karp, J. Soc. Indust. Appl. Math., 10 (1962), pp. 196--210]. ($O^*(f(n…

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