On Sets of Line Segments Featuring a Cactus Structure

被引：1

作者：

Brimkov, Boris ^{[1
]}

机构：

[1] Rice Univ, Computat & Appl Math, Houston, TX 77005 USA

来源：

COMBINATORIAL IMAGE ANALYSIS, IWCIA 2017 | 2017年 / 10256卷

基金：

美国国家科学基金会;

关键词：

Set of segments; Cactus graph; Segment intersections; Segment cycle; IN-PLACE; ALGORITHMS; INTERSECTION; GRAPHS;

D O I：

10.1007/978-3-319-59108-7_3

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper we derive sharp upper and lower bounds on the number of intersections and closed regions that can occur in a set of line segments whose underlying planar graph is a cactus graph. These bounds can be used to evaluate the complexity of certain algorithms for problems defined on sets of segments in terms of the cardinality of the segment sets. In particular, we give an application in the problem of finding a path between two points in a set of segments which travels through a minimum number of segments.

引用

页码：30 / 39

页数：10

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