带宽和失真再探

摘要：

在本文中，我们合并最近的发展，精确的算法，找到一个给定的图，最大限度地减少带宽（带宽问题）的顶点排序，并找到一个给定的图嵌入到一条线，最大限度地减少失真（失真问题）。对于这两个问题，我们开发了在O（9.363^n）时间和多项式空间中工作的算法。对于BANDWIDTH，这改进了Feige和Kilian从2000年开始的O^*（10^n）算法，对于DISTORTION，这是我们所知道的第一个在O（c^n）时间内工作的多项式空间精确算法。作为副产品，我们将Fomin等人的O（5^{n+o（n）}）-时间和O^*（2^n）-空间DISTORTION算法增强为O（4.383^n）时间和空间的算法。

英文摘要：

In this paper we merge recent developments on exact algorithms for finding an ordering of vertices of a given graph that minimizes bandwidth (the BANDWIDTH problem) and for finding an embedding of a given graph into a line that minimizes distortion (the DISTORTION problem). For both problems we develop algorithms that work in O(9.363^n) time and polynomial space. For BANDWIDTH, this improves O^*(10^n) algorithm by Feige and Kilian from 2000, for DISTORTION this is the first polynomial space exact algorithm that works in O(c^n) time we are aware of. As a byproduct, we enhance the O(5^{n+o(n)})-time and O^*(2^n)-space algorithm for DISTORTION by Fomin et al. to an algorithm working in O(4.383^n) time and space.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。