文章基本信息
- 标题：An Asymptotically Fast Polynomial Space Algorithm for Hamiltonicity Detection in Sparse Directed Graphs
- 本地全文：下载
- 作者：Andreas Björklund
- 期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
- 电子版ISSN：1868-8969
- 出版年度：2021
- 卷号：187
- 页码：15:1-15:12
- DOI：10.4230/LIPIcs.STACS.2021.15
- 出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
- 摘要：We present a polynomial space Monte Carlo algorithm that given a directed graph on n vertices and average outdegree δ, detects if the graph has a Hamiltonian cycle in 2^{n-Ω(n/δ)} time. This asymptotic scaling of the savings in the running time matches the fastest known exponential space algorithm by Björklund and Williams ICALP 2019. By comparison, the previously best polynomial space algorithm by Kowalik and Majewski IPEC 2020 guarantees a 2^{n-Ω(n/(2^δ))} 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 Björklund, 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 â"¤â,, from Björklund and Husfeldt FOCS 2013.
- 关键词：Hamiltonian cycle; directed graph; worst case analysis algorithm
