{"title":"交叉最小化满足同时绘图","authors":"Markus Chimani, M. Jünger, Michael Schulz","doi":"10.1109/PACIFICVIS.2008.4475456","DOIUrl":null,"url":null,"abstract":"We define the concept of crossing numbers for simultaneous graphs by extending the crossing number problem of traditional graphs. We discuss differences to the traditional crossing number problem, and give an NP-completeness proof and lower and upper bounds for the new problem. Furthermore, we show how existing heuristic and exact algorithms for the traditional problem can be adapted to the new task of simultaneous crossing minimization, and report on a brief experimental study of their implementations.","PeriodicalId":364669,"journal":{"name":"2008 IEEE Pacific Visualization Symposium","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2008-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":"{\"title\":\"Crossing Minimization meets Simultaneous Drawing\",\"authors\":\"Markus Chimani, M. Jünger, Michael Schulz\",\"doi\":\"10.1109/PACIFICVIS.2008.4475456\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We define the concept of crossing numbers for simultaneous graphs by extending the crossing number problem of traditional graphs. We discuss differences to the traditional crossing number problem, and give an NP-completeness proof and lower and upper bounds for the new problem. Furthermore, we show how existing heuristic and exact algorithms for the traditional problem can be adapted to the new task of simultaneous crossing minimization, and report on a brief experimental study of their implementations.\",\"PeriodicalId\":364669,\"journal\":{\"name\":\"2008 IEEE Pacific Visualization Symposium\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"25\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 IEEE Pacific Visualization Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/PACIFICVIS.2008.4475456\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 IEEE Pacific Visualization Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PACIFICVIS.2008.4475456","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We define the concept of crossing numbers for simultaneous graphs by extending the crossing number problem of traditional graphs. We discuss differences to the traditional crossing number problem, and give an NP-completeness proof and lower and upper bounds for the new problem. Furthermore, we show how existing heuristic and exact algorithms for the traditional problem can be adapted to the new task of simultaneous crossing minimization, and report on a brief experimental study of their implementations.