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Discret. Comput. Geom.最新文献

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Capture bounds for visibility-based pursuit evasion 基于可见性的追捕逃避的捕获边界
Discret. Comput. Geom. Pub Date : 2013-06-17 DOI: 10.1145/2462356.2462364
Kyle Klein, S. Suri
{"title":"Capture bounds for visibility-based pursuit evasion","authors":"Kyle Klein, S. Suri","doi":"10.1145/2462356.2462364","DOIUrl":"https://doi.org/10.1145/2462356.2462364","url":null,"abstract":"We investigate the following problem in the visibility-based discrete-time model of pursuit evasion in the plane: how many pursuers are needed to capture an evader in a polygonal environment with obstacles under the minimalist assumption that pursuers and the evader have the same maximum speed? When the environment is a simply-connected (hole-free) polygon of n vertices, we show that Θ (√n) pursuers are both necessary and sufficient in the worst-case. When the environment is a polygon with holes, we prove a lower bound of Ω (n2/3) and an upper bound of O(n5/6) for the number of pursuers that are needed in the worst-case, where n is the total number of vertices including the hole boundaries. More precisely, if the polygon contains h holes, our upper bound is O(n1/2 h1/4), for h ≤ n2/3, and O(n1/3 h1/2) otherwise. These bounds show that capture with minimal assumptions requires significantly more pursuers than what is possible either for visibility detection where pursuers win if one of them can see the evader [Guibas et al. 1999], or for capture when players' movement speed is small compared to \"features\" of the environment [Klein and Suri, 2012].","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"1 1","pages":"205-220"},"PeriodicalIF":0.0,"publicationDate":"2013-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88467246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 25
Fast segment insertion and incremental construction of constrained delaunay triangulations 约束delaunay三角剖分的快速分段插入和增量构造
Discret. Comput. Geom. Pub Date : 2013-06-17 DOI: 10.1145/2462356.2462389
J. Shewchuk, Brielin C. Brown
{"title":"Fast segment insertion and incremental construction of constrained delaunay triangulations","authors":"J. Shewchuk, Brielin C. Brown","doi":"10.1145/2462356.2462389","DOIUrl":"https://doi.org/10.1145/2462356.2462389","url":null,"abstract":"The most commonly implemented method of constructing a constrained Delaunay triangulation (CDT) in the plane is to first construct a Delaunay triangulation, then incrementally insert the input segments one by one. For typical implementations of segment insertion, this method has a Θ(kn2) worst-case running time, where n is the number of input vertices and k is the number of input segments. We give a randomized algorithm for inserting a segment into a CDT in expected time linear in the number of edges the segment crosses, and demonstrate with a performance comparison that it is faster than gift-wrapping for segments that cross many edges. A result of Agarwal, Arge, and Yi implies that randomized incremental construction of CDTs by our segment insertion algorithm takes expected O(n log n + n log2 k) time. We show that this bound is tight by deriving a matching lower bound. Although there are CDT construction algorithms guaranteed to run in O(n log n) time, incremental CDT construction is easier to program and competitive in practice. Moreover, the ability to incrementally update a CDT by inserting a segment is useful in itself.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"43 1","pages":"554-574"},"PeriodicalIF":0.0,"publicationDate":"2013-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77797178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 21
Homological reconstruction and simplification in R3 R3中的同调重构与化简
Discret. Comput. Geom. Pub Date : 2013-06-17 DOI: 10.1145/2462356.2462373
D. Attali, Ulrich Bauer, O. Devillers, M. Glisse, A. Lieutier
{"title":"Homological reconstruction and simplification in R3","authors":"D. Attali, Ulrich Bauer, O. Devillers, M. Glisse, A. Lieutier","doi":"10.1145/2462356.2462373","DOIUrl":"https://doi.org/10.1145/2462356.2462373","url":null,"abstract":"We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology of some complex H*(X) with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"13 1","pages":"606-621"},"PeriodicalIF":0.0,"publicationDate":"2013-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89321093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
On the Complexity of Barrier Resilience for Fat Regions 论脂肪区屏障弹性的复杂性
Discret. Comput. Geom. Pub Date : 2013-02-19 DOI: 10.1007/978-3-642-45346-5_15
Matias Korman, M. Löffler, Rodrigo I. Silveira, Darren Strash
{"title":"On the Complexity of Barrier Resilience for Fat Regions","authors":"Matias Korman, M. Löffler, Rodrigo I. Silveira, Darren Strash","doi":"10.1007/978-3-642-45346-5_15","DOIUrl":"https://doi.org/10.1007/978-3-642-45346-5_15","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"120 1","pages":"34-51"},"PeriodicalIF":0.0,"publicationDate":"2013-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87828630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
A Polynomial-Time Approximation Scheme for the Geometric Unique Coverage Problem on Unit Squares 单位平方上几何唯一覆盖问题的一个多项式时间逼近格式
Discret. Comput. Geom. Pub Date : 2012-07-04 DOI: 10.1007/978-3-642-31155-0_3
Takehiro Ito, Shin-Ichi Nakano, Y. Okamoto, Y. Otachi, Ryuhei Uehara, T. Uno, Yushi Uno
{"title":"A Polynomial-Time Approximation Scheme for the Geometric Unique Coverage Problem on Unit Squares","authors":"Takehiro Ito, Shin-Ichi Nakano, Y. Okamoto, Y. Otachi, Ryuhei Uehara, T. Uno, Yushi Uno","doi":"10.1007/978-3-642-31155-0_3","DOIUrl":"https://doi.org/10.1007/978-3-642-31155-0_3","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"1 1","pages":"25-39"},"PeriodicalIF":0.0,"publicationDate":"2012-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82381815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
Point-set embeddings of plane 3-trees 平面3-树的点集嵌入
Discret. Comput. Geom. Pub Date : 2012-04-01 DOI: 10.1016/J.COMGEO.2011.09.002
R. Nishat, Debajyoti Mondal, M. S. Rahman
{"title":"Point-set embeddings of plane 3-trees","authors":"R. Nishat, Debajyoti Mondal, M. S. Rahman","doi":"10.1016/J.COMGEO.2011.09.002","DOIUrl":"https://doi.org/10.1016/J.COMGEO.2011.09.002","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"28 1","pages":"88-98"},"PeriodicalIF":0.0,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89923687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
Routing multi-class traffic flows in the plane 路由平面上的多类流量
Discret. Comput. Geom. Pub Date : 2012-04-01 DOI: 10.1016/j.comgeo.2011.09.003
Joondong Kim, Joseph S. B. Mitchell, V. Polishchuk, Shang Yang, Jingyu Zou
{"title":"Routing multi-class traffic flows in the plane","authors":"Joondong Kim, Joseph S. B. Mitchell, V. Polishchuk, Shang Yang, Jingyu Zou","doi":"10.1016/j.comgeo.2011.09.003","DOIUrl":"https://doi.org/10.1016/j.comgeo.2011.09.003","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"45 1","pages":"99-114"},"PeriodicalIF":0.0,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88137941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
The Ordinary Line Problem Revisited 再看平线问题
Discret. Comput. Geom. Pub Date : 2012-04-01 DOI: 10.1016/j.comgeo.2011.10.003
A. Mukhopadhyay, Eugene Greene
{"title":"The Ordinary Line Problem Revisited","authors":"A. Mukhopadhyay, Eugene Greene","doi":"10.1016/j.comgeo.2011.10.003","DOIUrl":"https://doi.org/10.1016/j.comgeo.2011.10.003","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"74 3 1","pages":"127-130"},"PeriodicalIF":0.0,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89197919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Note on Interference in Random Networks 随机网络中的干扰问题
Discret. Comput. Geom. Pub Date : 2012-02-27 DOI: 10.1016/j.comgeo.2017.10.006
L. Devroye, Pat Morin
{"title":"A Note on Interference in Random Networks","authors":"L. Devroye, Pat Morin","doi":"10.1016/j.comgeo.2017.10.006","DOIUrl":"https://doi.org/10.1016/j.comgeo.2017.10.006","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"480 1","pages":"2-10"},"PeriodicalIF":0.0,"publicationDate":"2012-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80144149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A polygon is determined by its angles 多边形是由它的角度决定的
Discret. Comput. Geom. Pub Date : 2011-10-01 DOI: 10.1016/j.comgeo.2011.04.003
Y. Disser, Matús Mihalák, P. Widmayer
{"title":"A polygon is determined by its angles","authors":"Y. Disser, Matús Mihalák, P. Widmayer","doi":"10.1016/j.comgeo.2011.04.003","DOIUrl":"https://doi.org/10.1016/j.comgeo.2011.04.003","url":null,"abstract":"","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"3 1","pages":"418-426"},"PeriodicalIF":0.0,"publicationDate":"2011-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87678462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 19
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