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Minimizing the sum of diameters efficiently

John Hershberger
1992 Computational geometry  
This paper considers the problem of partitioning a planar set of n points into two subsets so that the sum of the diameters of the subsets is minimized.  ...  In the case in which the ratio between the diameter and the minimum inter-point distance of the set is polynomial in it, a refinement of our algorithm runs in optimal O(n log n) time. 09257721/92/$05.00  ...  Acknowledgment Thanks to Subhash Suri for several helpful and enjoyable discussions about this work, and to a perceptive referee who improved the content of the paper.  ... 
doi:10.1016/0925-7721(92)90028-q fatcat:bfsgdvgcifgznlrfqi52yt7exe

Fast computation of generalized Voronoi diagrams using graphics hardware

Kenneth E. Hoff, John Keyser, Ming Lin, Dinesh Manocha, Tim Culver
1999 Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99  
We generalize to weighted and farthest-site Voronoi diagrams, and present efficient techniques for computing the Voronoi boundaries, Voronoi neighbors, and the Delaunay triangulation of points.  ...  We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site.  ...  We would also like to thank Sarah Hoff for extensive help with editing and color plates, Chris Weigle for suggesting mosaicing using 2D point Voronoi diagrams, the UNCwalkthrough group for the house model  ... 
doi:10.1145/311535.311567 dblp:conf/siggraph/HoffKLMC99 fatcat:rt3plrqconhbddkbnjjhkeyroa

Fast computation of generalized Voronoi diagrams using graphics hardware

Kenneth E. Hoff, Tim Culver, John Keyser, Ming Lin, Dinesh Manocha
2000 Proceedings of the sixteenth annual symposium on Computational geometry - SCG '00  
We generalize to weighted and farthest-site Voronoi diagrams, and present efficient techniques for computing the Voronoi boundaries, Voronoi neighbors, and the Delaunay triangulation of points.  ...  We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site.  ...  We would also like to thank Sarah Hoff for extensive help with editing and color plates, Chris Weigle for suggesting mosaicing using 2D point Voronoi diagrams, the UNCwalkthrough group for the house model  ... 
doi:10.1145/336154.336226 dblp:conf/compgeom/HoffCKLM00 fatcat:hmk2drwkurfivjphezzzqx46aq

Net-Aware Critical Area Extraction for Opens in VLSI Circuits Via Higher-Order Voronoi Diagrams

Evanthia Papadopoulou
2011 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
Then the critical area extraction problem gets reduced to the construction of a generalized Voronoi diagram for open faults, based on concepts of higher order Voronoi diagrams.  ...  The approach expands the Voronoi critical area computation paradigm [1]-[7] with the ability to accurately compute critical area for missing material defects even in the presence of loops and redundant  ...  The region of C is denoted reg(C) and it is further subdivided into finer subregions by the farthest Voronoi diagram of C. For any point t ∈ reg(C), d(t, C) = max{d(t, c), ∀c ∈ C}.  ... 
doi:10.1109/tcad.2010.2100550 fatcat:x52b6fpw2fdjnenjzla4axzzgm

On Some Proximity Problems of Colored Sets [chapter]

Chenglin Fan, Jun Luo, Farong Zhong
2013 Lecture Notes in Computer Science  
We also give an optimal algorithm for the all farthest foreign neighbor problem (AFFN) in the plane, and propose algorithms to answer the farthest foreign neighbor query (FFNQ) of colored sets in two and  ...  The maximum diameter color-spanning set problem (MaxDCS) is defined as follows: given n points with m colors, select m points with m distinct colors such that the diameter of the set of chosen points is  ...  regions in F P V D(P \ E j ) which contradicts the property of Voronoi diagram, that is the region controlled by each point in farthest point Voronoi diagram should be connected.  ... 
doi:10.1007/978-3-319-03780-6_18 fatcat:j45gjwcz7bdhvioal6gud5ed6e

On Some Proximity Problems of Colored Sets

Cheng-Lin Fan, Jun Luo, Wen-Cheng Wang, Fa-Rong Zhong, Binhai Zhu
2014 Journal of Computer Science and Technology  
We also give an optimal algorithm for the all farthest foreign neighbor problem (AFFN) in the plane, and propose algorithms to answer the farthest foreign neighbor query (FFNQ) of colored sets in two and  ...  The maximum diameter color-spanning set problem (MaxDCS) is defined as follows: given n points with m colors, select m points with m distinct colors such that the diameter of the set of chosen points is  ...  regions in F P V D(P \ E j ) which contradicts the property of Voronoi diagram, that is the region controlled by each point in farthest point Voronoi diagram should be connected.  ... 
doi:10.1007/s11390-014-1475-0 fatcat:3nfy74ddh5fnvmflg6uklkrmw4

Quantum Computation in Computational Geometry

Kunihiko SADAKANE, Noriko SUGAWARA, Takeshi TOKUYAMA
2002 Interdisciplinary Information Sciences  
We discuss applications of quantum computation to geometric data processing.  ...  Technically, we apply well-known Grover's algorithm (and its variants) combined with geometric algorithms, and no further knowledge of quantum computing is required.  ...  Also they thank Takashi Mihara and Peter H(yer for valuable comments on an initial version of the paper.  ... 
doi:10.4036/iis.2002.129 fatcat:uxi6c5szrfbefiqx6dhdzpllt4

Visualization Tool [chapter]

2017 Encyclopedia of GIS  
Cross-References Distance Metrics Voronoi Diagrams for Query Processing Voronoi Terminology Synonyms Network voronoi; Voronoi-based query processing in road network databases Definition Query processing  ...  Cross-References Distance Metrics Voronoi Diagram Voronoi Diagrams for Query Processing Voronoi Tesselation Voronoi Diagram Voronoi-Based Query Processing in Road Network Databases Voronoi Diagrams  ...  data structures for efficient OSR query processing.  ... 
doi:10.1007/978-3-319-17885-1_101469 fatcat:rnvtcucz6vfulmc6voflfymen4

Coverage and connectivity issues in wireless sensor networks: A survey

Amitabha Ghosh, Sajal K. Das
2008 Pervasive and Mobile Computing  
Coverage and connectivity together can be treated as a measure of quality of service in a sensor network; it tells us how well each point in the region is covered and how accurate is the information gathered  ...  Acknowledgments The authors would like to thank Professor Bhaskar Krishnamachari of the Autonomous Networks Research Group at USC for his valuable inputs.  ...  We also sincerely thank the reviewers for constructive comments, which helped us to significantly improve the technical quality and organization of the paper.  ... 
doi:10.1016/j.pmcj.2008.02.001 fatcat:s3xoyljajvc2vmo3me2oc757by

Efficient algorithms for the minimum diameter bridge problem

Takeshi Tokuyama
2003 Computational geometry  
We give efficient algorithms for constructing a bridge between two convex regions in a fixed dimensional space so that the diameter of the bridged region is minimized.  ...  If both the set of vertices and the set of halfspaces defining the facets of the convex regions are given, we have an optimal linear time algorithm.  ...  He also thanks Xuehou Tan for inspiring discussion.  ... 
doi:10.1016/s0925-7721(02)00045-7 fatcat:yng7uc6l3ng5poazhdipw3mal4

Efficient algorithms for the minimum diameter bridge problem [chapter]

Takeshi Tokuyama
2001 Lecture Notes in Computer Science  
We give efficient algorithms for constructing a bridge between two convex regions in a fixed dimensional space so that the diameter of the bridged region is minimized.  ...  If both the set of vertices and the set of halfspaces defining the facets of the convex regions are given, we have an optimal linear time algorithm.  ...  He also thanks Xuehou Tan for inspiring discussion.  ... 
doi:10.1007/3-540-47738-1_34 fatcat:junnkvoqwrf6jknop7c2p6nsey

Spectral-Driven Isometry-Invariant Matching of 3D Shapes

Mauro R. Ruggeri, Giuseppe Patanè, Michela Spagnuolo, Dietmar Saupe
2009 International Journal of Computer Vision  
These critical points are invariant to isometries and are used as anchor points of a sampling technique, which extends the farthest point sampling by using statistical criteria for controlling the density  ...  Once a set of reference points has been computed, for each of them we construct a point-based statistical descriptor (PSSD, for short) of the input surface.  ...  We thank the anonymous reviewers for their comments and suggestions.  ... 
doi:10.1007/s11263-009-0250-0 fatcat:edw7v4jsrjbfvdxctumqm6kfgm

Chapter 7 A survey of computational geometry [chapter]

Joseph S.B. Mitchell, Subhash Suri
1995 Handbooks in Operations Research and Management Science  
The structures covered are convex hulls, arrangements, geometric duality, Voronoi diagram, and point location data structures.  ...  Suri incidences between a set of lines and a set of points, and counting the number of lines that bisect a set of points.  ...  For instance, if Voronoi diagrams are used for answering \nearest neighbor" queries, one needs to locate the Voronoi polyhedron containing the query point.  ... 
doi:10.1016/s0927-0507(05)80124-0 fatcat:nogmdqmv6bflni3waox5dxrsiy

On a Method of Multivariate Density Estimate Basedon Nearest Neighbours Graphs
Об одном методе оценки многомерной плотности на основеближайших соседей

G. Beliakov
2018 RUDN Journal of Mathematics Information Sciences and Physics  
The neighbours of a point lying in nearly the same direction are treated as redundant, and the contribution of the farthest neighbour is transferred to the nearer neighbour.  ...  The calculation of the local point density estimate is performed by the discrete Choquet integral, so that the contributions of the neighbours all around that point are accounted for.  ...  By applying mathematical induction, these properties are maintained till the end of the iterative reweighting process. The formula (4) expresses the end result of the described reweighting process.  ... 
doi:10.22363/2312-9735-2018-26-1-58-73 fatcat:fshmhlhdnnarjbk67msm3pclze

Efficient Sample Location Selection for Query Zone in Geo-Social Networks

Kejian Tang, Shaohui Zhan, Tao Zhan, Hui Zhu, Qian Zeng, Ming Zhong, Xiaoyu Zhu, Yuanyuan Zhu, Jianxin Li, Tieyun Qian, Rosa M. Benito
2021 Complexity  
Our experimental results on two real datasets demonstrate the effectiveness and efficiency of the proposed methods.  ...  Specifically, the online seeding performance is sensitive to the distance between the promoted location and its nearest sample location, and the offline precomputation performance is sensitive to the number  ...  To further accelerate the process, we propose CFLS that achieves a quick start.  ... 
doi:10.1155/2021/2581288 fatcat:4xjow32lbzfnphubd6wmthbwuy
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