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Improved Algorithms for Uniform Partitions of Points

Agarwal, Bhattacharya, Sen
2002 Algorithmica  
In this paper we consider the problem of partitioning a set of points in R 1 or R 2 into equal-size buckets, so that the maximum number of points in a bucket is minimized.  ...  Suppose at most (n/b) + points lie in each bucket in an optimal solution. We present algorithms whose time complexities depend on b and . No prior knowledge of is necessary for our algorithms.  ...  We first describe a deterministic O(n 4/3 log 2+ε n)-time algorithm, for any ε > 0, that computes an optimal uniform projection for the special case b = 2, thereby improving upon the quadratic upper-bound  ... 
doi:10.1007/s00453-001-0084-9 fatcat:22xvi4mqwnhtxma5wkykbbqk6q

Differential Private Spatial Decomposition and Location Publishing Based on Unbalanced Quadtree Partition Algorithm

Yan Yan, xin Gao, Adnan Mahmood, Tao Feng, Pengshou Xie
2020 IEEE Access  
An unbalanced quadtree partition algorithm based on regional uniformity is proposed.  ...  Experimental comparison of the real-world datasets proves the advantages of the proposed algorithm in improving the querying accuracy of the published data.  ...  On the contrary, for dense areas, adaptive grid partition would be performed to improve publishing accuracy.  ... 
doi:10.1109/access.2020.2999580 fatcat:bac4wewh6jcxdih6rkflt2md44

Numerical construction of optimal adaptive grids in two spatial dimensions

Tsu-Fen Chen, Haw-Dai Yang
2000 Computers and Mathematics with Applications  
Numerical results of model problems illustrating the efficiency of the proposed scheme are presented. Comparisons of the solutions with an existing scheme will also be provided.  ...  This article concerns a new procedure to generate a solution-adaptive grid for convection dominated problems in two spatial dimensions based on finite element approximations.  ...  Initial grids: 9 x 9 uniform grids; z = s/a. Exact solution (line) vs. numerical solutions of grid points on the flow line for Problem 1 when number of partitions A4 = 8 (0) and M = 16 (+).  ... 
doi:10.1016/s0898-1221(00)00133-4 fatcat:ejtaqk7skzhsdhr3izfimior6i

Profile-based partition for parallel simulation of DEVS-FIRE

Song Guo, Xiaolin Hu
2010 Proceedings of the 2010 Spring Simulation Multiconference on - SpringSim '10  
In previous work of wildfire spread simulation using DEVS-FIRE, we explored an approach of uniform spatial partition for supporting parallel simulation.  ...  The profile-based partition uses the ignition sequence of the forest cells as a profile to guide the partition of the cellular space for parallel simulation of DEVS-FIRE.  ...  of the locations of the ignition point for both uniform spatial partition and profile-based partition.  ... 
doi:10.1145/1878537.1878699 fatcat:anonvzug4zavjftfvratrann7y

AN IMPROVED PARALLEL ALGORITHM FOR DELAUNAY TRIANGULATION ON DISTRIBUTED MEMORY PARALLEL COMPUTERS

SANGYOON LEE, CHAN-IK PARK, CHAN-MO PARK
2001 Parallel Processing Letters  
In this paper, we propose an improved parallel algorithm for Delaunay triangulation, which partitions the bounding convex region of the input points set int o a n umber of regions by using Delaunay edges  ...  Partitioning by Delaunay edges makes it possible to eliminate merging step required for integrating subresults.  ...  All these improvements are possible by using projection-based partitioning methods. We consider Delaunay triangulation of points in just E 2 space.  ... 
doi:10.1142/s0129626401000634 fatcat:gglh72flrjcxzajtbyqjljfhri

Efficient Declustering of Non-uniform Multidimensional Data Using Shifted Hilbert Curves [chapter]

Hak-Cheol Kim, Mario A. Lopez, Scott T. Leutenegger, Ki-Joune Li
2004 Lecture Notes in Computer Science  
To decluster non-uniform data, a distribution sensitive bucketing algorithm is crucial for achieving good performance.  ...  Our experimental results show that the proposed declustering algorithm achieves a performance improvement up to 5 times relative to the two leading algorithms.  ...  Acknowledgments This work was supported by KOSEF grants number 01-2002-000-10014-0, by KOSEF grants number R05-2002-000-01288-0, by program for cultivating graduate students in regional strategic industry  ... 
doi:10.1007/978-3-540-24571-1_62 fatcat:twft6xhbyfbbzjvtfhxgf42wqi

A Unified Framework for Clustering Constrained Data without Locality Property [chapter]

Hu Ding, Jinhui Xu
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
Let P be an unknown set of points in R d . Let P = ∪ j l=1 P l be an unknown partition of P into j subsets. Let o l be the known mean point of P l for 1 ≤ l ≤ j.  ...  Peeling + Sampling Two novel techniques: A Peeling + Enclosing algorithm which outputs a set of candidates for k mean/median points.3 Algorithms for selecting the best candidate based on each  ...  Simplex Lemma A unified constant approximation Peeling + Enclosing 2 Selection algorithm for each individual constraint 3 Open problems Is it possible to improve the time complexity of the unified framework  ... 
doi:10.1137/1.9781611973730.97 dblp:conf/soda/DingX15 fatcat:h5odt42wwrbwxegrg4sjneklgi

Comparing synopsis techniques for approximate spatial data analysis

A. B. Siddique, Ahmed Eldawy, Vagelis Hristidis
2019 Proceedings of the VLDB Endowment  
The increasing amount of spatial data calls for new scalable query processing techniques.  ...  This paper experimentally studies four spatial data synopsis techniques for three common data analysis problems, namely, selectivity estimation, k-means clustering, and spatial partitioning.  ...  An image clustering algorithm [24] utilizes non-uniform histograms of the data distribution to improve image segmentation.  ... 
doi:10.14778/3342263.3342635 fatcat:pnck7eixezg6lmovat3oy4ushe

Edge-based Non-uniform Light Field Mapping

Wendong Wang, Baocai Yin, Dehui Kong
2003 International Conference on Digital Image Computing: Techniques and Applications  
In this paper, an image-based method---non-uniform light field mapping is proposed which combines edge-based surface light field partition and non-uniform decomposition of light field matrixes for real-time  ...  Finally, we present an image-based rendering method which improves rendering performance through textures sorting and rendering directly from these compact data with the support of graphic card.  ...  Acknowledgments We would like to thank Wei-Chao Chen at UNC for providing their raw data for our use.  ... 
dblp:conf/dicta/WangYK03 fatcat:f54nosvfgbaxnbrunbk26dvw54

On the convergence and sampling of randomized primal-dual algorithms and their application to parallel MRI reconstruction [article]

Eric B Gutierrez, Claire Delplancke, Matthias J Ehrhardt
2022 arXiv   pre-print
The Stochastic Primal-Dual Hybrid Gradient or SPDHG is an algorithm proposed by Chambolle et al. to efficiently solve a wide class of nonsmooth large-scale optimization problems.  ...  We show that the sampling can significantly affect the convergence speed of SPDHG. We conclude that for many cases an optimal sampling method can be identified.  ...  EBG acknowledges the Mexican Council of Science and Technology (CONACyT).  ... 
arXiv:2207.12291v1 fatcat:t67hleklj5bp5a6mmgipzgptte

Farthest-point optimized point sets with maximized minimum distance

Thomas Schlömer, Daniel Heck, Oliver Deussen
2011 Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics - HPG '11  
The second is a variant of the main algorithm that partitions any point set into equally sized subsets, each with large mutual distances; the resulting partitionings yield improved results in more general  ...  optimization of a random point set with 1024 points.  ...  Acknowledgments We thank the anonymous reviewers for their in-depth reviews and valuable suggestions for improvement.  ... 
doi:10.1145/2018323.2018345 dblp:conf/egh/SchlomerHD11 fatcat:3vh6j7i4gbdodlakffgxoafqsq

Spatial Statistic Data Release Based on Differential Privacy

2019 KSII Transactions on Internet and Information Systems  
The traditional data-dependent partition methods need to allocate a part of the privacy budgets for the partitioning process and split the budget among all the steps, which is inefficient.  ...  Second, we perform IH-Tree (Improved H-Tree) partition on the synthetic dataset and use the resulting partition keys to split the original dataset.  ...  The [10] points out that the query accuracy will be significantly improved if more budget is allocated for node count than for medians.  ... 
doi:10.3837/tiis.2019.10.023 fatcat:n5h2hl5znvay3akna7iprz7o3a

Consistency of Spectral Partitioning of Uniform Hypergraphs under Planted Partition Model

Debarghya Ghoshdastidar, Ambedkar Dukkipati
2014 Neural Information Processing Systems  
The analysis reveals that the algorithm is consistent for m-uniform hypergraphs for larger values of m, and also the rate of convergence improves for increasing m.  ...  In this paper, we view these models as random m-uniform hypergraphs and establish the consistency of spectral algorithm in this general setting.  ...  Such a tensor based approach was first studied in [7] for geometric grouping. Subsequent improvements of the algorithm were proposed in [22, 20] .  ... 
dblp:conf/nips/GhoshdastidarD14 fatcat:pyizzyai65fbfikbp5ckbc7ope

An image-to-answer algorithm for fully automated digital PCR image processing

Zhiqiang Yan, Haoqing Zhang, Xinlu Wang, Martina Ganova, Tomas Lednicky, Hanliang Zhu, Xiaocheng Liu, Marie Korabecna, Honglong Chang, Pavel Neuzil
2022 Lab on a Chip  
Digital polymerase chain reaction (dPCR) is an irreplaceable variant of PCR techniques due to its capacity for absolute quantification and detection of rare deoxyribonucleic acid (DNA) sequences in clinical  ...  LTACH19005 from the Ministry of Education, Youth, and Sports of the Czech Republic and grant no. RVO-VFN 64165 from the Ministry of Health of the Czech Republic. We also  ...  Acknowledgements Haoqing Zhang, Zhiqiang Yan, Xinlu Wang, and Pavel Neužil were supported by grant no. 2018YFE0109000 from the Ministry of Science and Technology of the P.R. of China.  ... 
doi:10.1039/d1lc01175h pmid:35258048 fatcat:u26i7k3fiff6pnifhxmsdv7jli

Achieving Differential Privacy Publishing of Location-Based Statistical Data Using Grid Clustering

Yan Yan, Zichao Sun, Adnan Mahmood, Fei Xu, Zhuoyue Dong, Quan Z. Sheng
2022 ISPRS International Journal of Geo-Information  
A bottom-up grid clustering algorithm is designed to perform on the blank and the uniform grids of the same density level based on neighborhood similarity.  ...  Statistical partitioning and publishing is commonly used in location-based big data services to address queries such as the number of points of interest, available vehicles, traffic flows, infected patients  ...  For the tree-based partition algorithms, the increase of partition gradually causes more recursive operations and uniformity judgments; therefore, the execution time of these algorithms suffers significantly  ... 
doi:10.3390/ijgi11070404 fatcat:nai375uivbbdrkokrau5ozp3pu
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