{"title":"覆盖多边形是困难的","authors":"J. Culberson, R. Reckhow","doi":"10.1109/SFCS.1988.21976","DOIUrl":null,"url":null,"abstract":"It is shown that the following minimum cover problems are NP-hard, even for polygons without holes: (1) covering an arbitrary polygon with convex polygons; (2) covering the boundary of an arbitrary polygon with convex polygons; (3) covering an orthogonal polygon with rectangles; and (4) covering the boundary of an orthogonal polygon with rectangles. It is noted that these results hold even if the polygons are required to be in general position.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"144 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"155","resultStr":"{\"title\":\"Covering polygons is hard\",\"authors\":\"J. Culberson, R. Reckhow\",\"doi\":\"10.1109/SFCS.1988.21976\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is shown that the following minimum cover problems are NP-hard, even for polygons without holes: (1) covering an arbitrary polygon with convex polygons; (2) covering the boundary of an arbitrary polygon with convex polygons; (3) covering an orthogonal polygon with rectangles; and (4) covering the boundary of an orthogonal polygon with rectangles. It is noted that these results hold even if the polygons are required to be in general position.<<ETX>>\",\"PeriodicalId\":113255,\"journal\":{\"name\":\"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science\",\"volume\":\"144 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"155\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1988.21976\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1988.21976","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is shown that the following minimum cover problems are NP-hard, even for polygons without holes: (1) covering an arbitrary polygon with convex polygons; (2) covering the boundary of an arbitrary polygon with convex polygons; (3) covering an orthogonal polygon with rectangles; and (4) covering the boundary of an orthogonal polygon with rectangles. It is noted that these results hold even if the polygons are required to be in general position.<>
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