Patrizio Angelini, M. Bekos, Fabrizio Montecchiani, Maximilian Pfister
{"title":"On morphs of 1-plane graphs","authors":"Patrizio Angelini, M. Bekos, Fabrizio Montecchiani, Maximilian Pfister","doi":"10.20382/jocg.v13i1a10","DOIUrl":"https://doi.org/10.20382/jocg.v13i1a10","url":null,"abstract":"","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79387825","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}
{"title":"Recognizing weighted and seeded disk graphs","authors":"Boris Klemz, M. Nöllenburg, Roman Prutkin","doi":"10.20382/jocg.v13i1a13","DOIUrl":"https://doi.org/10.20382/jocg.v13i1a13","url":null,"abstract":"","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91023427","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}
1 We show in this note how to interpret logarithmic spiral tilings as one-dimensional particle 2 systems undergoing inelastic collapse. By deforming the spirals appropriately, we can simulate 3 collisions among particles with distinct or varying coefficients of restitution. Our geometric 4 constructions provide a strikingly simple illustration of a widely studied phenomenon in the 5 physics of dissipative gases: the collapse of inelastic particles. 6 Lines 154
{"title":"A Geometric Approach to Inelastic Collapse","authors":"Yufei Zheng, Kritkorn Karntikoon, B. Chazelle","doi":"10.20382/jocg.v13i1a7","DOIUrl":"https://doi.org/10.20382/jocg.v13i1a7","url":null,"abstract":"1 We show in this note how to interpret logarithmic spiral tilings as one-dimensional particle 2 systems undergoing inelastic collapse. By deforming the spirals appropriately, we can simulate 3 collisions among particles with distinct or varying coefficients of restitution. Our geometric 4 constructions provide a strikingly simple illustration of a widely studied phenomenon in the 5 physics of dissipative gases: the collapse of inelastic particles. 6 Lines 154","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"13 1","pages":"197-203"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79970081","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}
Matthijs Ebbens, I. Iordanov, M. Teillaud, G. Vegter
The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincaré disk model, under the action of the group generated by the hyperbolic isometries identifying opposite sides of a regular octagon centered at the origin. We consider generalized Bolza surfaces Mg, where the octagon is replaced by a regular 4g-gon, leading to a genus g surface. We propose an extension of Bowyer’s algorithm to these surfaces. In particular, we compute the value of the systole of Mg. We also propose algorithms computing small sets of points on Mg that are used to initialize Bowyer’s algorithm.
{"title":"Delaunay triangulations of generalized Bolza surfaces","authors":"Matthijs Ebbens, I. Iordanov, M. Teillaud, G. Vegter","doi":"10.20382/jocg.v13i1a5","DOIUrl":"https://doi.org/10.20382/jocg.v13i1a5","url":null,"abstract":"The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincaré disk model, under the action of the group generated by the hyperbolic isometries identifying opposite sides of a regular octagon centered at the origin. We consider generalized Bolza surfaces Mg, where the octagon is replaced by a regular 4g-gon, leading to a genus g surface. We propose an extension of Bowyer’s algorithm to these surfaces. In particular, we compute the value of the systole of Mg. We also propose algorithms computing small sets of points on Mg that are used to initialize Bowyer’s algorithm.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"28 1","pages":"125-177"},"PeriodicalIF":0.0,"publicationDate":"2021-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79313769","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}
The well-separated pair decomposition (WSPD) of the complete Euclidean graph defined on points in $R^2$, introduced by Callahan and Kosaraju [JACM, 42 (1): 67-90, 1995], is a technique for partitioning the edges of the complete graph based on length into a linear number of sets. Among the many different applications of WSPDs, Callahan and Kosaraju proved that the sparse subgraph that results by selecting an arbitrary edge from each set (called WSPD-spanner) is a $1 + 8/(s − 4)$-spanner, where $s > 4$ is the separation ratio used for partitioning the edges.Although competitive local-routing strategies exist for various spanners such as Yao-graphs, $Theta$-graphs, and variants of Delaunay graphs, few local-routing strategies are known for any WSPD-spanner. Our main contribution is a local-routing algorithm with a near-optimal competitive routing ratio of $1 + O(1/s)$ on a WSPD-spanner.Specifically, using Callahan and Kosaraju’s fair split-tree, we show how to build a WSPD-spanner with spanning ratio $1 + 4/s + 4/(s − 2)$ which is a slight improvement over $1 + 8/(s − 4)$. We then present a 2-local and a 1-local routing algorithm on this spanner with competitive routing ratios of $1 + 6/(s − 2) + 4/s$ and $1 + 8/(s − 2) + 4/s + 8/s^2$, respectively. Moreover, we prove that there exists a point set for which our WSPD-spanner has a spanning ratio of at least $1 + 8/s$, thereby proving the near-optimality of its spanning ratio and the near-optimality of the routing ratio of both our routing algorithms.
{"title":"Local routing in WSPD-based spanners","authors":"J. Carufel, P. Bose, F. Paradis, V. Dujmovic","doi":"10.20382/JOCG.V12I1A1","DOIUrl":"https://doi.org/10.20382/JOCG.V12I1A1","url":null,"abstract":"The well-separated pair decomposition (WSPD) of the complete Euclidean graph defined on points in $R^2$, introduced by Callahan and Kosaraju [JACM, 42 (1): 67-90, 1995], is a technique for partitioning the edges of the complete graph based on length into a linear number of sets. Among the many different applications of WSPDs, Callahan and Kosaraju proved that the sparse subgraph that results by selecting an arbitrary edge from each set (called WSPD-spanner) is a $1 + 8/(s − 4)$-spanner, where $s > 4$ is the separation ratio used for partitioning the edges.Although competitive local-routing strategies exist for various spanners such as Yao-graphs, $Theta$-graphs, and variants of Delaunay graphs, few local-routing strategies are known for any WSPD-spanner. Our main contribution is a local-routing algorithm with a near-optimal competitive routing ratio of $1 + O(1/s)$ on a WSPD-spanner.Specifically, using Callahan and Kosaraju’s fair split-tree, we show how to build a WSPD-spanner with spanning ratio $1 + 4/s + 4/(s − 2)$ which is a slight improvement over $1 + 8/(s − 4)$. We then present a 2-local and a 1-local routing algorithm on this spanner with competitive routing ratios of $1 + 6/(s − 2) + 4/s$ and $1 + 8/(s − 2) + 4/s + 8/s^2$, respectively. Moreover, we prove that there exists a point set for which our WSPD-spanner has a spanning ratio of at least $1 + 8/s$, thereby proving the near-optimality of its spanning ratio and the near-optimality of the routing ratio of both our routing algorithms.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"52 1","pages":"1-34"},"PeriodicalIF":0.0,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84669485","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}
We investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms.
{"title":"Approximating Minimum-Area Rectangular and Convex Containers for Packing Convex Polygons","authors":"H. Alt, M. D. Berg, Christian Knauer","doi":"10.20382/jocg.v8i1a1","DOIUrl":"https://doi.org/10.20382/jocg.v8i1a1","url":null,"abstract":"We investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"48 1","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85744765","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}
{"title":"An explicit PL-embedding of the square flat torus into $mathbb{E}^3$","authors":"Tanessí Quintanar","doi":"10.20382/JOCG.V11I1A24","DOIUrl":"https://doi.org/10.20382/JOCG.V11I1A24","url":null,"abstract":"We present an explicit PL-embedding of the flat square torus $mathbb{T}^2=mathbb{E}^2/mathbb{Z}^2$ into $mathbb{E}^3$, with 40 vertices and 80 faces.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"30 1","pages":"615-628"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77340804","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：