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AHD: The alternate hierarchical decomposition of nonconvex polytopes (generalization of a convex polytope based spatial data model)

R. Bulbul, A.U. Frank
2009 2009 17th International Conference on Geoinformatics  
Our approach decomposes the given nonconvex polytope with arbitrary genus into a set of component convex hulls, which are represented hierarchically in a tree structure, convex hull tree, CHT.  ...  to any dimension.  ...  This is achievable if the procedure for computing convex hull is dimension independent. For this any of the existing dimension independent convex hull algorithms [28, 29] can be used. D.  ... 
doi:10.1109/geoinformatics.2009.5293499 fatcat:gf3f5nukevbvhpj2awwpz3vdbi

A Novel and Efficient Method for Testing Non Linear Separability [chapter]

David Elizondo, Juan Miguel Ortiz-de-Lazcano-Lobato, Ralph Birkenhead
2007 Lecture Notes in Computer Science  
This test is based on the convex hull separability method but does not require the computation of the convex hull.  ...  A fast and efficient test for non linear separability is proposed which can be used to pretest classification data sets for non linear separability thus avoiding expensive computations.  ...  The 2 class 2 dimension classification problem shown in figure 2-a will be used to illustrate the Convex Hull separability algorithm.  ... 
doi:10.1007/978-3-540-74690-4_75 fatcat:ok3zx3s7szafnj7nfp74pe5hvm


Laura Vyšniauskaitė, Vydūnas Šaltenis
2006 Technological and Economic Development of Economy  
Besides, two new algorithms have been created and presented. The experiment research has shown a very good efficiency of these algorithms.  ...  Convex hull is the minimum area convex polygon containing the planar set.  ...  The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S.  ... 
doi:10.3846/13928619.2006.9637764 fatcat:vy6xbnxgu5am5gzs4uy3qzh7mu

Parallel algorithms in geometry [chapter]

Michael Goodrich
2004 Handbook of Discrete and Computational Geometry, Second Edition  
Is there an efficient output-sensitive parallel convex hull algorithm for d ≥ 4?3. Is there an optimal-work O(log 2 n)-time CREW PRAM convex hull algorithm for odd dimensions greater than 4?  ...  Assign a processor to each pair of sublists and compute the common upper tangent line for the two upper convex hulls for these two lists, which can be done in O(log n) time using a well-known "binary search  ... 
doi:10.1201/9781420035315.ch42 fatcat:bjv5rzaoxne5tjle6ppvondlam

On Geometric Structure of Activation Spaces in Neural Networks [article]

Yuting Jia, Haiwen Wang, Shuo Shao, Huan Long, Yunsong Zhou, Xinbing Wang
2019 arXiv   pre-print
We propose an efficient approximation algorithm to characterize the convex hull of massive points in high dimensional space.  ...  We believe our work reveals several critical intrinsic properties of modern neural networks and further gives a new metric for evaluating them.  ...  A new efficient approximate convex hull algorithm in high dimensions In this section, we propose our algorithm for finding the convex hull of high dimensional points, which is called Revised Greedy Expansion  ... 
arXiv:1904.01399v1 fatcat:mvrvgyabenhmzflqlhjcyi57sq

An Efficient Index Building Algorithm for Selection of Aggregator Nodes in Wireless Sensor Networks

Sun-Young Ihm, Aziz Nasridinov, Young-Ho Park
2014 International Journal of Distributed Sensor Networks  
Thus, we propose an efficient index building algorithm for selection of aggregator nodes, called the Approximate Convex Hull Index (simply, aCH-Index).  ...  and then computes the convex hull in each subregion.  ...  In this paper, we propose an efficient index building algorithm for selection of aggregator nodes.  ... 
doi:10.1155/2014/520428 fatcat:7b3qxvrelvbedlwrou2xrronyu

Solving the Multidimensional Multiple-choice Knapsack Problem by constructing convex hulls

Md Mostofa Akbar, M. Sohel Rahman, M. Kaykobad, E.G. Manning, G.C. Shoja
2006 Computers & Operations Research  
Convex hulls are constructed to reduce the search space to find the near-optimal solution of the MMKP. We present the computational complexity of solving the MMKP using this approach.  ...  We apply a transformation technique to map the multidimensional resource consumption to single dimension.  ...  Acknowledgements The authors would like to express their gratitude to the anonymous referees for their helpful comments and suggestions.  ... 
doi:10.1016/j.cor.2004.09.016 fatcat:njhukdioi5fgrpxfganxjzl7ia

Faster geometric algorithms via dynamic determinant computation

Vissarion Fisikopoulos, Luis Peñaranda
2016 Computational geometry  
We propose two dynamic determinant algorithms with quadratic arithmetic complexity when employed in convex hull and volume computations, and with linear arithmetic complexity when used in point location  ...  The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location.  ...  Emiris for his advice and encouragement, Elias Tsigaridas for bibliographic suggestions, Menelaos Karavelas for discussions on efficient dynamic determinant updates and Olivier Devillers for discussions  ... 
doi:10.1016/j.comgeo.2015.12.001 fatcat:4zbrgfjo6remxcm4ftniq2wvwi

Reverse Furthest Neighbors in Spatial Databases

Bin Yao, Feifei Li, Piyush Kumar
2009 Proceedings / International Conference on Data Engineering  
Our approach takes advantage of the furthest Voronoi diagrams as well as the convex hulls of either the data set P (in the MRFN case) or the query set Q (in the BRFN case).  ...  This paper presents the challenges associated with such queries and proposes efficient, R-tree based algorithms for both monochromatic and bichromatic versions of the RFN queries.  ...  P's convex hull: There are I/O efficient algorithms for computing the convex hulls of disk-based data sets.  ... 
doi:10.1109/icde.2009.62 dblp:conf/icde/YaoLK09 fatcat:3gq66oikhbhalbkwc2ngg52jv4

Algorithm for Computing Convex Skyline Objectsets on Numerical Databases

Md. Anisuzzaman SIDDIQUE, Yasuhiko MORIMOTO
2010 IEICE transactions on information and systems  
The number of sets in the database amounts to n C s . We propose an efficient algorithm to compute convex skyline of the n C s sets.  ...  We consider a skyline query for sets of objects in a database in this paper. Let s be the number of objects in each set and n be the number of objects in the database.  ...  Algorithm for Convex Skyline Objectsets In this section, we present an algorithm for computing convex skyline s-objectsets.  ... 
doi:10.1587/transinf.e93.d.2709 fatcat:d3mdiirdhbg4pjhlq4p63oyxoy

Fast Convex Layers Algorithm for Near-Duplicate Image Detection

Smiljan Šinjur, Damjan Zazula, Borut Žalik
2012 Informatica  
This paper builds on a novel, fast algorithm for generating the convex layers on grid points with linear time complexity. Convex layers are extracted from the binary image.  ...  The obtained convex hulls are characterized by the number of their vertices and used as representative image features.  ...  Conclusion In this paper, a novel computationally efficient algorithm for image matching was presented. The method determines a set of convex hulls for every image to be compared.  ... 
doi:10.15388/informatica.2012.379 fatcat:jrph4penwbbdzkv36q3ngivnk4

Convex hull ranking algorithm for multi-objective evolutionary algorithms

M. Davoodi Monfared, A. Mohades, J. Rezaei
2011 Scientia Iranica. International Journal of Science and Technology  
This new algorithm, called the Convex Hull Ranking Algorithm (CHRA), uses geometric objects, like convex hull and onion layers, and is very suitable for convex MOOPs.  ...  Then, we use convex hull concepts to present a new ranking procedure for multi-objective evolutionary algorithms.  ...  One fast algorithm for computing the convex hull is the Quick Hull [19] . This algorithm can be efficiently used for finding each quarter part of a convex hull.  ... 
doi:10.1016/j.scient.2011.08.017 fatcat:s4q4h535kvcexp7n6ksch4fhmi

Efficient Representation and Computation of Reachable Sets for Hybrid Systems [chapter]

Olaf Stursberg, Bruce H. Krogh
2003 Lecture Notes in Computer Science  
Computing reachable sets is an essential step in most analysis and synthesis techniques for hybrid systems.  ...  The orientations keep the over-approximation of the reachable sets small in most cases with a complexity of low polynomial order with respect to the dimension of the continuous state space.  ...  Acknowledgment This research has been financially supported in part by the U.S. Army Research Office and the U.S. Defense Advanced Projects Research Agency.  ... 
doi:10.1007/3-540-36580-x_35 fatcat:bmqyzx27qncexpshfegdg6a7qa

Fast Two Dimensional Convex Hull on the GPU

Srikanth Srungarapu, Durga Prasad Reddy, Kishore Kothapalli, P.J. Narayanan
2011 2011 IEEE Workshops of International Conference on Advanced Information Networking and Applications  
In this paper, we present a GPU-optimized implementation for finding the convex hull of a two dimensional point set. Our implementation tries to minimize the impact of irregular data access patterns.  ...  GPGPU is best suited for regular data parallel algorithms. They are not directly amenable for algorithms which have irregular data access patterns such as convex hull, list ranking etc.  ...  As explained earlier, the quick hull algorithm can be easily extended to higher dimensions. So we wish to implement convex hull on higher dimensions in future.  ... 
doi:10.1109/waina.2011.64 dblp:conf/aina/SrungarapuRKN11 fatcat:i3j2nwrz7rgvpj3a7ht5mpkzni

Large data sets classification using convex–concave hull and support vector machine

Asdrúbal López Chau, Xiaoou Li, Wen Yu
2012 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
Then, we use Jarvis march method to determine the concave (non-convex) hull for the inseparable points. Finally, the vertices of the convex-concave hull are applied for SVM training.  ...  This paper introduces a novel method for SVM classification, called convex-concave hull SVM (CCH-SVM). After grid processing, the convex hull is used to find extreme points.  ...  Multi-dimensional case In order to extend convex-concave hull to more than two dimensions, the dimension reduction is necessary.  ... 
doi:10.1007/s00500-012-0954-x fatcat:oyzpvqlsqrc4hcdeg2fpioieti
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