Subexponential Algorithms for Rectilinear Steiner Tree and Arborescence Problems

F. Fomin, Sudeshna Kolay, D. Lokshtanov, Fahad Panolan, Saket Saurabh
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引用次数: 14

Abstract

A rectilinear Steiner tree for a set K of points in the plane is a tree that connects k using horizontal and vertical lines. In the Rectilinear Steiner Tree problem, the input is a set K={z1,z2,…, zn} of n points in the Euclidean plane (R2), and the goal is to find a rectilinear Steiner tree for k of smallest possible total length. A rectilinear Steiner arborescence for a set k of points and a root r ∈ K is a rectilinear Steiner tree T for K such that the path in T from r to any point z ∈ K is a shortest path. In the Rectilinear Steiner Arborescence problem, the input is a set K of n points in R2, and a root r ∈ K, and the task is to find a rectilinear Steiner arborescence for K, rooted at r of smallest possible total length. In this article, we design deterministic algorithms for these problems that run in 2O(√ nlog n) time.
线性Steiner树和树形问题的次指数算法
平面上有K个点的直线斯坦纳树是用水平线和垂直线把K点连接起来的树。在线性斯坦纳树问题中,输入是欧几里得平面(R2)上n个点的集合K={z1,z2,…,zn},目标是找到K总长度最小的线性斯坦纳树。对于k个点和根r∈k的集合,一个线性斯坦纳树形是k的线性斯坦纳树T,使得T中从r到任意点z∈k的路径是最短路径。在线性斯坦纳树形问题中,输入是R2中n个点的集合K,其根r∈K,任务是求出K的一个总长度最小的、根在r的直线斯坦纳树形。在本文中,我们为这些问题设计了确定性算法,运行时间为20(√nlog n)。
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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