International Journal of Computational Geometry and Applications最新文献_第2页

On Covering Points with Minimum Turns 关于用最小匝数覆盖点

International Journal of Computational Geometry and Applications Pub Date : 2012-05-14 DOI: 10.1142/s0218195915500016

Minghui Jiang

引用次数: 11

On the discrete Unit Disk Cover Problem 关于离散单元磁盘盖问题

International Journal of Computational Geometry and Applications Pub Date : 2011-02-18 DOI: 10.1142/S0218195912500094

G. Das, Robert Fraser, A. López-Ortiz, B. Nickerson

引用次数: 73

Multi Cover of a Polygon Minimizing the Sum of Areas 多边形的多重覆盖最小化面积总和

International Journal of Computational Geometry and Applications Pub Date : 2011-02-18 DOI: 10.1142/S021819591100386X

A. K. Abu-Affash, Paz Carmi, M. J. Katz, G. Morgenstern

引用次数: 18

Constrained Point-Set Embeddability of Planar Graphs 平面图的约束点集嵌入性

International Journal of Computational Geometry and Applications Pub Date : 2009-02-05 DOI: 10.1007/978-3-642-00219-9_35

E. D. Giacomo, W. Didimo, G. Liotta, H. Meijer, S. Wismath

引用次数: 7

Covering a Point Set by Two Disjoint Rectangles 覆盖由两个不相交的矩形组成的点集

International Journal of Computational Geometry and Applications Pub Date : 2008-12-15 DOI: 10.1142/S0218195911003676

Sang-Sub Kim, S. Bae, Hee-Kap Ahn

引用次数: 10

Free-Form Surface Partition in 3-d 三维自由曲面分割

International Journal of Computational Geometry and Applications Pub Date : 2008-12-15 DOI: 10.1142/S0218195911003834

D. Chen, Ewa Misiolek

{"title":"Free-Form Surface Partition in 3-d","authors":"D. Chen, Ewa Misiolek","doi":"10.1142/S0218195911003834","DOIUrl":"https://doi.org/10.1142/S0218195911003834","url":null,"abstract":"We study the problem of partitioning a spherical representation S of a free-form surface F in 3-D, which is to partition a 3-D sphere S into two hemispheres such that a representative normal vector for each hemisphere optimizes a given global objective function. This problem arises in important practical applications, particularly surface machining in manufacturing. We model the spherical surface partition problem as processing multiple off-line sequences of insertions/deletions of convex polygons alternated with certain point queries on the common intersection of the polygons. Our algorithm combines nontrivial data structures, geometric observations, and algorithmic techniques. It takes $O(min{m^2n log log m + frac{m^3 log^2(mn) log^2(log m)}{log^3 m}, m^3log^2n+mn})$ time, where m is the number of polygons, of size O(n) each, in one off-line sequence (generally, m ≤ n). This is a significant improvement over the previous best-known O(m 2 n 2) time algorithm. As a by-product, our algorithm can process O(n) insertions/deletions of convex polygons (of size O(n) each) and queries on their common intersections in O(n 2 loglogn) time, improving over the \"standard\" O(n 2 logn) time solution for off-line maintenance of O(n 2) insertions/deletions of points and queries. Our techniques may be useful in solving other problems.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123371462","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: 7

Approximate Nearest Neighbor Search under Translation Invariant Hausdorff Distance 平移不变Hausdorff距离下的近似最近邻搜索

International Journal of Computational Geometry and Applications Pub Date : 2008-12-15 DOI: 10.1142/S0218195911003706

Christian Knauer, Marc Scherfenberg

{"title":"Approximate Nearest Neighbor Search under Translation Invariant Hausdorff Distance","authors":"Christian Knauer, Marc Scherfenberg","doi":"10.1142/S0218195911003706","DOIUrl":"https://doi.org/10.1142/S0218195911003706","url":null,"abstract":"The Hausdorff distance is a measure for the resemblance of two geometric objects. Given a set of n point patterns and a query point pattern Q , the nearest neighbor of Q under the Hausdorff distance is the point pattern which minimizes this distance to Q . An extension of the Hausdorff distance is the translation invariant Hausdorff distance which additionally allows the translation of the point patterns in order to minimize the distance. This paper introduces the first data structure which allows to solve the nearest neighbor problem for the directed Hausdorff distance under translation in sublinear query time in a non-heuristic manner, in the sense that the quality of the results, the performance, and the space bounds are guaranteed. The data structure answers queries for both directions of the directed Hausdorff distance with a $ sqrt{d(s-1.5)}(1+epsilon) $-approximation factor in $ O(log frac{n}{epsilon}) $ query time for the nearest neighbor and O(k + logn) query time for the k -th nearest neighbor for any e> 0 . (The O -notation of the latter runtime contains terms that are quadratic in e -1 .) \u0000 \u0000Furthermore it is shown how to find the exact nearest neighbor under the directed Hausdorff distance without transformation of the point sets within some weaker time and storage bounds.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133532853","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: 3

Finding Popular Places 寻找热门地点

International Journal of Computational Geometry and Applications Pub Date : 2007-12-17 DOI: 10.1142/S0218195910003189

M. Benkert, B. Djordjevic, Joachim Gudmundsson, T. Wolle

引用次数: 40

On Minimum Area Planar Upward Drawings of Directed Trees and Other Families of Directed Acyclic Graphs 有向树及其他有向无环图族的最小面积平面向上图

International Journal of Computational Geometry and Applications Pub Date : 2007-06-21 DOI: 10.1142/S021819590800260X

Fabrizio Frati

{"title":"On Minimum Area Planar Upward Drawings of Directed Trees and Other Families of Directed Acyclic Graphs","authors":"Fabrizio Frati","doi":"10.1142/S021819590800260X","DOIUrl":"https://doi.org/10.1142/S021819590800260X","url":null,"abstract":"It has been shown in [9] that there exist planar digraphs that require exponential area in every upward straight-line planar drawing. On the other hand, upward poly-line planar drawings of planar graphs can be realized in Θ(n2) area [9]. In this paper we consider families of DAGs that naturally arise in practice, like DAGs whose underlying graph is a tree (directed trees), is a bipartite graph (directed bipartite graphs), or is an outerplanar graph (directed outerplanar graphs). Concerning directed trees, we show that optimal Θ(n log n) area upward straight-line/polyline planar drawings can be constructed. However, we prove that if the order of the neighbors of each node is assigned, then exponential area is required for straight-line upward drawings and quadratic area is required for poly-line upward drawings, results surprisingly and sharply contrasting with the area bounds for planar upward drawings of undirected trees. After having established tight bounds on the area requirements of planar upward drawings of several families of directed trees, we show how the results obtained for trees can be exploited to determine asymptotic optimal values for the area occupation of planar upward drawings of directed bipartite graphs and directed outerplanar graphs.","PeriodicalId":285210,"journal":{"name":"International Journal of Computational Geometry and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129306457","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: 10

Optimal Construction of the City Voronoi Diagram 城市Voronoi图的优化构建

International Journal of Computational Geometry and Applications Pub Date : 2006-12-18 DOI: 10.1142/S021819590900285X

S. Bae, Jae-Hoon Kim, Kyung-Yong Chwa

引用次数: 23