{"title":"平面图形的内矩形图","authors":"Kazuyuki Miura, Hiroki Haga, Takao Nishizeki","doi":"10.1142/S0218195906002026","DOIUrl":null,"url":null,"abstract":"A drawing of a plane graph is called an inner rectangular drawing if every edge is drawn as a horizontal or vertical line segment so that every inner face is a rectangle In this paper we show that a plane graph G has an inner rectangular drawing D if and only if a new bipartite graph constructed from G has a perfect matching We also show that D can be found in time O(n1.5/log n) if G has n vertices and a sketch of the outer face is prescribed, that is, all the convex outer vertices and concave ones are prescribed.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"Inner Rectangular Drawings of Plane Graphs\",\"authors\":\"Kazuyuki Miura, Hiroki Haga, Takao Nishizeki\",\"doi\":\"10.1142/S0218195906002026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A drawing of a plane graph is called an inner rectangular drawing if every edge is drawn as a horizontal or vertical line segment so that every inner face is a rectangle In this paper we show that a plane graph G has an inner rectangular drawing D if and only if a new bipartite graph constructed from G has a perfect matching We also show that D can be found in time O(n1.5/log n) if G has n vertices and a sketch of the outer face is prescribed, that is, all the convex outer vertices and concave ones are prescribed.\",\"PeriodicalId\":285210,\"journal\":{\"name\":\"International Journal of Computational Geometry and Applications\",\"volume\":\"21 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computational Geometry and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/S0218195906002026\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computational Geometry and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/S0218195906002026","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 16
摘要
平面图的绘制叫做内部矩形图如果每个边缘画作为一个水平或垂直的线段,这样每一个内表面都是矩形在本文中,我们表明,平面图G有一个内在的矩形图D当且仅当一个新的两偶图由G有一个完美的匹配我们可以发现还表明,D O (n1.5 / O (log n))如果G n顶点和草图的外脸规定,也就是说,所有的外凸顶点和内凹顶点都是规定的。
A drawing of a plane graph is called an inner rectangular drawing if every edge is drawn as a horizontal or vertical line segment so that every inner face is a rectangle In this paper we show that a plane graph G has an inner rectangular drawing D if and only if a new bipartite graph constructed from G has a perfect matching We also show that D can be found in time O(n1.5/log n) if G has n vertices and a sketch of the outer face is prescribed, that is, all the convex outer vertices and concave ones are prescribed.
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