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

共 50 条

[21] AN O(N LOG N) ALGORITHM FOR THE ALL-NEAREST-NEIGHBORS PROBLEM
VAIDYA, PM
DISCRETE & COMPUTATIONAL GEOMETRY, 1989, 4 (02) : 101 - 115
[22] An O(n3 log log n/log n) time algorithm for the all-pairs shortest path problem
Takaoka, T
INFORMATION PROCESSING LETTERS, 2005, 96 (05) : 155 - 161
[23] An O(n√n, log log n) average case algorithm for the maximum induced matching problem in permutation graphs
Viet Cuong Than
Phan Thuan Do
PROCEEDINGS OF THE 2018 5TH ASIAN CONFERENCE ON DEFENSE TECHNOLOGY (ACDT 2018), 2018, : 45 - 49
[24] An O(n log2 n) algorithm for a sink location problem in dynamic tree networks
Mamada, S
Uno, T
Makino, K
Fujishige, S
EXPLORING NEW FRONTIERS OF THEORETICAL INFORMATICS, 2004, 155 : 251 - 264
[25] A practical O(n log2 n) time algorithm for computing the triplet distance on binary trees
Sand, Andreas
Brodal, Gerth Stolting
Fagerberg, Rolf
Pedersen, Christian N. S.
Mailund, Thomas
BMC BIOINFORMATICS, 2013, 14
[26] A practical O(n log2n) time algorithm for computing the triplet distance on binary trees
Andreas Sand
Gerth Stølting Brodal
Rolf Fagerberg
Christian NS Pedersen
Thomas Mailund
BMC Bioinformatics, 14
[27] An O(n(3) log log n/log(2) n) time algorithm for all pairs shortest paths
Han, Yijie
Takaoka, Tadao
JOURNAL OF DISCRETE ALGORITHMS, 2016, 38-41 : 9 - 19
[28] An O(n log n) algorithm for the maximum agreement subtree problem for binary trees
Cole, R
Colton, MF
Hariharan, R
Przytycka, T
Thorup, M
SIAM JOURNAL ON COMPUTING, 2000, 30 (05) : 1385 - 1404
[29] An O(n3(log log n/log n)5/4) time algorithm for all pairs shortest paths
Han, Yijie
ALGORITHMS - ESA 2006, PROCEEDINGS, 2006, 4168 : 411 - 417
[30] AN O (n log n)-TIME ALGORITHM FOR THE k-CENTER PROBLEM IN TREES
Wang, Haitao
Zhang, Jingru
SIAM JOURNAL ON COMPUTING, 2021, 50 (02) : 602 - 635

← 1 2 3 4 5 →