{"title":"On Counting Monotone Polygons and Holes in a Point Set","authors":"Sang-Won Bae","doi":"10.5626/jcse.2023.17.3.109","DOIUrl":null,"url":null,"abstract":"In this paper, we study the problem of counting the number of monotone polygons in a given set S of n points in general position in the plane. A simple polygon is said to be monotone when any vertical line intersects its boundary at most twice. To our best knowledge, this counting problem remains unsolved and no nontrivial algorithm is known so far. As a research step forward to tackle the problem, we define a subclass of monotone polygons and present the first efficient algorithms that exactly count them.","PeriodicalId":37773,"journal":{"name":"Journal of Computing Science and Engineering","volume":"50 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computing Science and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5626/jcse.2023.17.3.109","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
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Abstract
In this paper, we study the problem of counting the number of monotone polygons in a given set S of n points in general position in the plane. A simple polygon is said to be monotone when any vertical line intersects its boundary at most twice. To our best knowledge, this counting problem remains unsolved and no nontrivial algorithm is known so far. As a research step forward to tackle the problem, we define a subclass of monotone polygons and present the first efficient algorithms that exactly count them.
期刊介绍：
Journal of Computing Science and Engineering (JCSE) is a peer-reviewed quarterly journal that publishes high-quality papers on all aspects of computing science and engineering. The primary objective of JCSE is to be an authoritative international forum for delivering both theoretical and innovative applied researches in the field. JCSE publishes original research contributions, surveys, and experimental studies with scientific advances. The scope of JCSE covers all topics related to computing science and engineering, with a special emphasis on the following areas: Embedded Computing, Ubiquitous Computing, Convergence Computing, Green Computing, Smart and Intelligent Computing, Human Computing.
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