Recognizing Map Graphs of Bounded Treewidth

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING Algorithmica Pub Date : 2023-10-27 DOI:10.1007/s00453-023-01180-6

Patrizio Angelini, Michael A. Bekos, Giordano Da Lozzo, Martin Gronemann, Fabrizio Montecchiani, Alessandra Tappini

引用次数: 0

Abstract

A map is a partition of the sphere into interior-disjoint regions homeomorphic to closed disks. Some regions are labeled as nations, while the remaining ones are labeled as holes. A map in which at most k nations touch at the same point is a k-map, while it is hole-free if it contains no holes. A graph is a map graph if there is a bijection between its vertices and the nations of a map, such that two nations touch if and only the corresponding vertices are connected by an edge. We present a fixed-parameter tractable algorithm for recognizing map graphs parameterized by treewidth. Its time complexity is linear in the size of the graph. It reports a certificate in the form of a so-called witness, if the input is a yes-instance. Our algorithmic framework is general enough to test, for any k, if the input graph admits a k-map or a hole-free k-map.

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识别有界树宽的地图图形

映射是将球面划分为与封闭磁盘同构的内部相邻区域。一些区域被标记为 "国"，而其余区域被标记为 "洞"。最多有 k 个国家在同一点接触的图是 k 图，如果不包含洞，则是无洞图。如果一个图的顶点与地图中的国家之间存在双投影关系，那么这个图就是一个地图图，只有相应的顶点通过边相连时，两个国家才会接触。我们提出了一种固定参数的可行算法，用于识别以树宽为参数的地图图。其时间复杂度与图的大小成线性关系。如果输入是一个 "是 "的实例，它就会以所谓 "证人 "的形式报告证书。我们的算法框架具有足够的通用性，对于任意 k，都能测试输入图是否包含 k 映射或无洞 k 映射。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.

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