哈维格数的计算及相关的收缩问题

ACM Transactions on Computation Theory (TOCT) Pub Date : 2020-04-24 DOI:10.1145/3448639

F. Fomin, D. Lokshtanov, Ivan Mihajlin, Saket Saurabh, M. Zehavi

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引用次数: 7

摘要

证明了n顶点图G的哈维格数(G中小团的最大大小)不能在时间no(n)内计算，除非指数时间假设(ETH)不成立。这解决了精确指数算法领域中一个众所周知的开放性问题。为解决哈维格数问题而开发的技术具有更广泛的适用性。我们用它来排除无(n)时间算法(到ETH)的存在，用于大量关于图中边收缩的计算问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Computation of Hadwiger Number and Related Contraction Problems

We prove that the Hadwiger number of an n-vertex graph G (the maximum size of a clique minor in G) cannot be computed in time no(n), unless the Exponential Time Hypothesis (ETH) fails. This resolves a well-known open question in the area of exact exponential algorithms. The technique developed for resolving the Hadwiger number problem has a wider applicability. We use it to rule out the existence of no(n)-time algorithms (up to the ETH) for a large class of computational problems concerning edge contractions in graphs.

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ACM Transactions on Computation Theory (TOCT)

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