{"title":"平面图形在线性时间内的双欧拉轨迹求解[CMOS VLSI电路设计]","authors":"Zhi-Zhong Chen, Xin He, Chun-Hsi Huang","doi":"10.1109/SFFCS.1999.814603","DOIUrl":null,"url":null,"abstract":"The paper answers an open question in the design of complimentary metal-oxide semiconductor (CMOS) VLSI circuits. It asks whether a polynomial-time algorithm can decide if a given planar graph has a plane embedding /spl epsiv/ such that /spl epsiv/ has a Euler trail P=e/sub 1/e/sub 2/...e/sub m/ and its dual graph has a Euler trail P*=e/sub 1/*e/sub 2/*...e/sub m/* where e/sub i/* is the dual edge of e/sub i/ for i=1, 2, ..., m. The paper answers this question in the affirmative by presenting a linear-time algorithm.","PeriodicalId":385047,"journal":{"name":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1999-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Finding double Euler trails of planar graphs in linear time [CMOS VLSI circuit design]\",\"authors\":\"Zhi-Zhong Chen, Xin He, Chun-Hsi Huang\",\"doi\":\"10.1109/SFFCS.1999.814603\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper answers an open question in the design of complimentary metal-oxide semiconductor (CMOS) VLSI circuits. It asks whether a polynomial-time algorithm can decide if a given planar graph has a plane embedding /spl epsiv/ such that /spl epsiv/ has a Euler trail P=e/sub 1/e/sub 2/...e/sub m/ and its dual graph has a Euler trail P*=e/sub 1/*e/sub 2/*...e/sub m/* where e/sub i/* is the dual edge of e/sub i/ for i=1, 2, ..., m. The paper answers this question in the affirmative by presenting a linear-time algorithm.\",\"PeriodicalId\":385047,\"journal\":{\"name\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-10-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFFCS.1999.814603\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFFCS.1999.814603","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Finding double Euler trails of planar graphs in linear time [CMOS VLSI circuit design]
The paper answers an open question in the design of complimentary metal-oxide semiconductor (CMOS) VLSI circuits. It asks whether a polynomial-time algorithm can decide if a given planar graph has a plane embedding /spl epsiv/ such that /spl epsiv/ has a Euler trail P=e/sub 1/e/sub 2/...e/sub m/ and its dual graph has a Euler trail P*=e/sub 1/*e/sub 2/*...e/sub m/* where e/sub i/* is the dual edge of e/sub i/ for i=1, 2, ..., m. The paper answers this question in the affirmative by presenting a linear-time algorithm.
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