构建多边形边界上平面图的平面图

IF 0.9 4区数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Combinatorial Optimization Pub Date : 2024-10-07 DOI:10.1007/s10878-024-01217-8

Rohit Lohani, Krishnendra Shekhawat

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引用次数: 0

摘要

平面图（F）是将多边形边界（P）分割成 n 个区域，满足 n 个顶点图给出的邻接关系。这里假定多边形边界的边平行于 x 轴或 y 轴，或者斜率为 1。对于给定的多边形边界 P（有 m 条线段）和平面三角形图 G，本文提出了一种线性时间算法，用于构建具有所需多边形边界的平面图，满足所有给定的邻接关系。此外，本文还证明了对于长度为 m 的给定多边形边界 P，所获得的平面图 (F) 中每个区域的边数最多为 m + 1（只有一个区域除外，该区域最多可有 m + 5 条边）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Construction of floorplans for plane graphs over polygonal boundaries

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Construction of floorplans for plane graphs over polygonal boundaries

A floorplan (F) is a partition of a polygonal boundary (P) into n-regions satisfying the adjacencies given by an n-vertex graph. Here, it is assumed that the sides of the polygonal boundary are either parallel to the x-axis or y-axis or have slopes \(-1\) or 1. For a given polygonal boundary P (having m line segments) and a plane triangulated graph G, this paper presents a linear-time algorithm for constructing a floorplan with the required polygonal boundary satisfying all given adjacencies. Further, it has been proved that the number of sides of each region in the obtained floorplan (F) is at most m + 1 (except one region, which can have at most m + 5 sides) for the given polygonal boundary P of length m.

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来源期刊

Journal of Combinatorial Optimization 数学-计算机：跨学科应用

CiteScore

2.00

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.