{"title":"建立矩形平面图的一种算法","authors":"Sany M. Leinwand, Y. Lai","doi":"10.1109/DAC.1984.1585874","DOIUrl":null,"url":null,"abstract":"Previous reports [1] [3] have shown how to build an optimal floor-plan assembly starting with a planar structure graph in terms of components and their connections. The existing methods are based on exhaustively inspecting all possible rectangular duals until an optimal one is found. However, expensive computational resources are wasted when no rectangular dual exists. This paper presents a graph-theoretical formulation for the existence of rectangular floor-plans. It is shown that any triangulated graph (planar graph with all regions triangular) admits a rectangular dual if and only if it does not contain complex triangular faces. This result is the basis of a fast algorithm for checking admissibility of solutions.","PeriodicalId":188431,"journal":{"name":"21st Design Automation Conference Proceedings","volume":"35 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1984-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"42","resultStr":"{\"title\":\"An Algorithm for Building Rectangular Floor-Plans\",\"authors\":\"Sany M. Leinwand, Y. Lai\",\"doi\":\"10.1109/DAC.1984.1585874\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Previous reports [1] [3] have shown how to build an optimal floor-plan assembly starting with a planar structure graph in terms of components and their connections. The existing methods are based on exhaustively inspecting all possible rectangular duals until an optimal one is found. However, expensive computational resources are wasted when no rectangular dual exists. This paper presents a graph-theoretical formulation for the existence of rectangular floor-plans. It is shown that any triangulated graph (planar graph with all regions triangular) admits a rectangular dual if and only if it does not contain complex triangular faces. This result is the basis of a fast algorithm for checking admissibility of solutions.\",\"PeriodicalId\":188431,\"journal\":{\"name\":\"21st Design Automation Conference Proceedings\",\"volume\":\"35 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1984-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"42\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"21st Design Automation Conference Proceedings\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DAC.1984.1585874\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"21st Design Automation Conference Proceedings","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DAC.1984.1585874","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Previous reports [1] [3] have shown how to build an optimal floor-plan assembly starting with a planar structure graph in terms of components and their connections. The existing methods are based on exhaustively inspecting all possible rectangular duals until an optimal one is found. However, expensive computational resources are wasted when no rectangular dual exists. This paper presents a graph-theoretical formulation for the existence of rectangular floor-plans. It is shown that any triangulated graph (planar graph with all regions triangular) admits a rectangular dual if and only if it does not contain complex triangular faces. This result is the basis of a fast algorithm for checking admissibility of solutions.
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