An O (n5/2 log n) algorithm for the Rectilinear Minimum Link-Distance Problem in three dimensions

被引：4

作者：

Wagner, David P. ^{[1
]}

Drysdale, Robert Scot ^{[2
]}

Stein, Clifford ^{[3
]}

机构：

[1] Korea Univ, Sch Elect Engn, Seoul, South Korea

[2] Dartmouth Coll, Dept Comp Sci, Hanover, NH 03755 USA

[3] Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2009年 / 42卷 / 05期

关键词：

Minimum link path; Rectilinear path; Shortest path; Binary space partition; Sweep plane; Segment tree; Priority queue; BINARY SPACE PARTITIONS; OBSTACLES; PATHS;

D O I：

10.1016/j.comgeo.2008.04.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the Rectilinear Minimum Link Path Problem among rectilinear obstacles in three dimensions. The problem is well studied in two dimensions, but is relatively unexplored in higher dimensions. We solve the problem in O(beta n log n) time, where n is the number of corners among all obstacles, and beta is the size of a binary space partition (BSP) decomposition of the space containing the obstacles. There exist methods to find a BSP where in the worst-case beta = Theta(n(3/2)), giving us an overall worst-case time of O (n(5/2) log n). Previously known algorithms have had worst-case running times of Omega(n(3)). (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：376 / 387

页数：12

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