Counting Cycles on Planar Graphs in Subexponential Time

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Algorithmica Pub Date : 2023-10-30 DOI:10.1007/s00453-023-01182-4

Jin-Yi Cai, Ashwin Maran

引用次数: 0

Abstract

We study the problem of counting all cycles or self- avoiding walks (SAWs) on triangulated planar graphs. We present a subexponential \(2^{O(\sqrt{n})}\) time algorithm for this counting problem. Among the technical ingredients used in this algorithm are the planar separator theorem and a delicate analysis using pairs of Motzkin paths and Motzkin numbers. We can then adapt this algorithm to uniformly sample SAWs, in subexponential time. Our work is motivated by the problem of gerrymandered districting maps.

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以亚指数时间计算平面图上的周期

我们研究了在三角形平面图上计算所有循环或自避行（SAW）的问题。我们为这个计数问题提出了一种亚指数(2^{O(\sqrt{n})}/)时间算法。该算法使用的技术要素包括平面分离定理以及使用莫兹金路径和莫兹金数对进行的精细分析。然后，我们可以调整该算法，在亚指数时间内对 SAW 进行均匀采样。我们的工作源于选区划分图问题。

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.