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- W3088462235 abstract "We present a polynomial space Monte Carlo algorithm that given a directed graph on $n$ vertices and average outdegree $delta$, detects if the graph has a Hamiltonian cycle in $2^{n-Omega(frac{n}{delta})}$ time. This asymptotic scaling of the savings in the running time matches the fastest known exponential space algorithm by Bjorklund and Williams ICALP 2019. By comparison, the previously best polynomial space algorithm by Kowalik and Majewski IPEC 2020 guarantees a $2^{n-Omega(frac{n}{2^delta})}$ time bound. Our algorithm combines for the first time the idea of obtaining a fingerprint of the presence of a Hamiltonian cycle through an inclusion--exclusion summation over the Laplacian of the graph from Bjorklund, Kaski, and Koutis ICALP 2017, with the idea of sieving for the non-zero terms in an inclusion--exclusion summation by listing solutions to systems of linear equations over $mathbb{Z}_2$ from Bjorklund and Husfeldt FOCS 2013." @default.
- W3088462235 created "2020-10-01" @default.
- W3088462235 creator A5038787166 @default.
- W3088462235 date "2020-09-24" @default.
- W3088462235 modified "2023-09-27" @default.
- W3088462235 title "An Asymptotically Fast Polynomial Space Algorithm for Hamiltonicity Detection in Sparse Directed Graphs" @default.
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