Monotone Paths in Geometric Triangulations

被引：1

作者：

Dumitrescu, Adrian ^{[1
]}

Mandal, Ritankar ^{[1
]}

Toth, Csaba D. ^{[2
,3
]}

机构：

[1] Univ Wisconsin, Milwaukee, WI 53201 USA

[2] Calif State Univ Northridge, Los Angeles, CA USA

[3] Tufts Univ, Medford, MA 02155 USA

来源：

Combinatorial Algorithms | 2016年 / 9843卷

基金：

美国国家科学基金会;

关键词：

Monotone path; Triangulation; Counting algorithm; SIMPLEX-ALGORITHM; HIRSCH CONJECTURE; PLANAR GRAPHS; RANDOM-EDGE; BOUNDS; NUMBER; CYCLES; MATCHINGS; POLYHEDRA;

D O I：

10.1007/978-3-319-44543-4_32

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

(I) We prove that the (maximum) number of monotone paths in a triangulation of n points in the plane is O(1.8027(n)). This improves an earlier upper bound of O(1.8393(n)); the current best lower bound is O(1.7034(n)). (II) Given a planar straight-line graph G with n vertices, we show that the number of monotone paths in G can be computed in O(n(2)) time.

引用

页码：411 / 422

页数：12

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