Discret. Comput. Geom.最新文献_第2页

Complexity Results on Untangling Red-Blue Matchings 解缠结红蓝匹配的复杂性结果

Discret. Comput. Geom. Pub Date : 2022-02-24 DOI: 10.1007/978-3-031-20624-5_44

Arunjana Das, Sandip Das, G. D. D. Fonseca, Y. Gérard, B. Rivier

引用次数: 2

A note on the minimum number of red lines needed to pierce the intersections of blue lines 关于穿过蓝线交叉处所需的最小红线数量的说明

Discret. Comput. Geom. Pub Date : 2022-01-01 DOI: 10.1016/j.comgeo.2022.101863

M. Huicochea, J. Leaños, Luis Manuel Rivera

引用次数: 0

Range Updates and Range Sum Queries on Multidimensional Points with Monoid Weights 一元权重多维点上的范围更新与范围和查询

Discret. Comput. Geom. Pub Date : 2022-01-01 DOI: 10.4230/LIPIcs.ISAAC.2022.57

Shangqi Lu, Yufei Tao

引用次数: 0

Shortest Rectilinear Path Queries to Rectangles in a Rectangular Domain 矩形域内矩形的最短直线路径查询

Discret. Comput. Geom. Pub Date : 2021-12-01 DOI: 10.1007/978-3-030-61792-9_22

Mincheol Kim, S. Yoon, Hee-Kap Ahn

引用次数: 0

Dynamic Data Structures for k-Nearest Neighbor Queries k近邻查询的动态数据结构

Discret. Comput. Geom. Pub Date : 2021-09-24 DOI: 10.4230/LIPIcs.ISAAC.2021.14

Sarita de Berg, F. Staals

{"title":"Dynamic Data Structures for k-Nearest Neighbor Queries","authors":"Sarita de Berg, F. Staals","doi":"10.4230/LIPIcs.ISAAC.2021.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2021.14","url":null,"abstract":"Our aim is to develop dynamic data structures that support $k$-nearest neighbors ($k$-NN) queries for a set of $n$ point sites in the plane in $O(f(n) + k)$ time, where $f(n)$ is some polylogarithmic function of $n$. The key component is a general query algorithm that allows us to find the $k$-NN spread over $t$ substructures simultaneously, thus reducing an $O(tk)$ term in the query time to $O(k)$. Combining this technique with the logarithmic method allows us to turn any static $k$-NN data structure into a data structure supporting both efficient insertions and queries. For the fully dynamic case, this technique allows us to recover the deterministic, worst-case, $O(log^2n/loglog n +k)$ query time for the Euclidean distance claimed before, while preserving the polylogarithmic update times. We adapt this data structure to also support fully dynamic emph{geodesic} $k$-NN queries among a set of sites in a simple polygon. For this purpose, we design a shallow cutting based, deletion-only $k$-NN data structure. More generally, we obtain a dynamic planar $k$-NN data structure for any type of distance functions for which we can build vertical shallow cuttings. We apply all of our methods in the plane for the Euclidean distance, the geodesic distance, and general, constant-complexity, algebraic distance functions.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"24 1","pages":"101976"},"PeriodicalIF":0.0,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76141256","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

Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model 代数决策树模型中若干3和难几何问题的次二次算法

Discret. Comput. Geom. Pub Date : 2021-09-15 DOI: 10.4230/LIPIcs.ISAAC.2021.3

B. Aronov, M. D. Berg, J. Cardinal, Esther Ezra, J. Iacono, M. Sharir

{"title":"Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model","authors":"B. Aronov, M. D. Berg, J. Cardinal, Esther Ezra, J. Iacono, M. Sharir","doi":"10.4230/LIPIcs.ISAAC.2021.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.ISAAC.2021.3","url":null,"abstract":"We present subquadratic algorithms in the algebraic decision-tree model for several textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise disjoint segments in the plane, and a set $C$ of $n$ triangles in the plane, we want to count, for each triangle $Deltain C$, the number of intersection points between the segments of $A$ and those of $B$ that lie in $Delta$. The problems considered in this paper have been studied by Chan~(2020), who gave algorithms that solve them, in the standard real-RAM model, in $O((n^2/log^2n)log^{O(1)}log n)$ time. We present solutions in the algebraic decision-tree model whose cost is $O(n^{60/31+varepsilon})$, for any $varepsilon>0$. Our approach is based on a primal-dual range searching mechanism, which exploits the multi-level polynomial partitioning machinery recently developed by Agarwal, Aronov, Ezra, and Zahl~(2020). A key step in the procedure is a variant of point location in arrangements, say of lines in the plane, which is based solely on the emph{order type} of the lines, a\"handicap\"that turns out to be beneficial for speeding up our algorithm.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"42 1","pages":"101945"},"PeriodicalIF":0.0,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84862050","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∞ Persistent Homology Estimates Detailed Topology from Pointcloud Datasets 点云数据集的一个∞持久同调估计详细拓扑

Discret. Comput. Geom. Pub Date : 2021-08-11 DOI: 10.1007/s00454-021-00319-y

Francisco Belchí Guillamón, Anastasios Stefanou

引用次数: 2

Routing by matching on convex pieces of grid graphs 在网格图的凸块上匹配路由

Discret. Comput. Geom. Pub Date : 2021-06-20 DOI: 10.1016/j.comgeo.2022.101862

H. Alpert, R. Barnes, S. Bell, A. Mauro, N. Nevo, N. Tucker, H. Yang

引用次数: 0

On the approximation of shortest escape paths 关于最短逃逸路径的近似

Discret. Comput. Geom. Pub Date : 2021-02-01 DOI: 10.1016/j.comgeo.2020.101709

David Kübel, E. Langetepe

引用次数: 1

Efficient Segment Folding is Hard 高效分段折叠困难

Discret. Comput. Geom. Pub Date : 2020-12-21 DOI: 10.1016/j.comgeo.2022.101860

T. Horiyama, Fabian Klute, Matias Korman, I. Parada, Ryuhei Uehara, Katsuhisa Yamanaka

引用次数: 0