Finding a shortest diagonal of a simple polygon in linear time

被引：1

作者：

Hershberger, J

Suri, S

机构：

[1] MENTOR GRAPH CORP,SAN JOSE,CA 95131

[2] WASHINGTON UNIV,DEPT COMP SCI,ST LOUIS,MO 63130

[3] BELLCORE,MORRISTOWN,NJ

[4] DEC,SYST RES CTR,PALO ALTO,CA

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 1997年 / 7卷 / 03期

关键词：

simple polygon; visibility; shortest diagonal; closest pair; window partition; matrix searching;

D O I：

10.1016/0925-7721(95)00032-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A diagonal of a planar, simple polygon P is an open line segment that connects two nonadjacent vertices and lies in the relative interior of P. We present a linear time algorithm for finding a shortest diagonal (in the L(2) norm) of a simple polygon, improving the previous best result by a factor of log n. Our result provides an interesting contrast to a known Omega(n log n) lower bound for finding a closest pair of vertices in a simple polygon-observe that a shortest diagonal is defined by a closest pair of vertices satisfying an additional visibility constraint.

引用

页码：149 / 160

页数：12

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