%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/DIMACS10/delaunay_n20
% name: DIMACS10/delaunay_n20
% [DIMACS10 set: delaunay/delaunay_n20]
% id: 2475
% date: 2011
% author: M. Holtgrewe, P. Sanders, C. Schulz
% ed: C. Schulz
% fields: name title A id date author ed kind notes
% kind: undirected graph
%-------------------------------------------------------------------------------
% notes:
% 10th DIMACS Implementation Challenge:                                   
%                                                                         
% http://www.cc.gatech.edu/dimacs10/index.shtml                           
%                                                                         
% As stated on their main website (                                       
% http://dimacs.rutgers.edu/Challenges/ ), the "DIMACS Implementation     
% Challenges address questions of determining realistic algorithm         
% performance where worst case analysis is overly pessimistic and         
% probabilistic models are too unrealistic: experimentation can provide   
% guides to realistic algorithm performance where analysis fails."        
%                                                                         
% For the 10th DIMACS Implementation Challenge, the two related           
% problems of graph partitioning and graph clustering were chosen.        
% Graph partitioning and graph clustering are among the aforementioned    
% questions or problem areas where theoretical and practical results      
% deviate significantly from each other, so that experimental outcomes    
% are of particular interest.                                             
%                                                                         
% Problem Motivation                                                      
%                                                                         
% Graph partitioning and graph clustering are ubiquitous subtasks in      
% many application areas. Generally speaking, both techniques aim at      
% the identification of vertex subsets with many internal and few         
% external edges. To name only a few, problems addressed by graph         
% partitioning and graph clustering algorithms are:                       
%                                                                         
%     * What are the communities within an (online) social network?       
%     * How do I speed up a numerical simulation by mapping it            
%         efficiently onto a parallel computer?                           
%     * How must components be organized on a computer chip such that     
%         they can communicate efficiently with each other?               
%     * What are the segments of a digital image?                         
%     * Which functions are certain genes (most likely) responsible       
%         for?                                                            
%                                                                         
% Challenge Goals                                                         
%                                                                         
%     * One goal of this Challenge is to create a reproducible picture    
%         of the state-of-the-art in the area of graph partitioning       
%         (GP) and graph clustering (GC) algorithms. To this end we       
%         are identifying a standard set of benchmark instances and       
%         generators.                                                     
%                                                                         
%     * Moreover, after initiating a discussion with the community, we    
%         would like to establish the most appropriate problem            
%         formulations and objective functions for a variety of           
%         applications.                                                   
%                                                                         
%     * Another goal is to enable current researchers to compare their    
%         codes with each other, in hopes of identifying the most         
%         effective algorithmic innovations that have been proposed.      
%                                                                         
%     * The final goal is to publish proceedings containing results       
%         presented at the Challenge workshop, and a book containing      
%         the best of the proceedings papers.                             
%                                                                         
% Problems Addressed                                                      
%                                                                         
% The precise problem formulations need to be established in the course   
% of the Challenge. The descriptions below serve as a starting point.     
%                                                                         
%     * Graph partitioning:                                               
%                                                                         
%       The most common formulation of the graph partitioning problem     
%       for an undirected graph G = (V,E) asks for a division of V into   
%       k pairwise disjoint subsets (partitions) such that all            
%       partitions are of approximately equal size and the edge-cut,      
%       i.e., the total number of edges having their incident nodes in    
%       different subdomains, is minimized. The problem is known to be    
%       NP-hard.                                                          
%                                                                         
%     * Graph clustering:                                                 
%                                                                         
%       Clustering is an important tool for investigating the             
%       structural properties of data. Generally speaking, clustering     
%       refers to the grouping of objects such that objects in the same   
%       cluster are more similar to each other than to objects of         
%       different clusters. The similarity measure depends on the         
%       underlying application. Clustering graphs usually refers to the   
%       identification of vertex subsets (clusters) that have             
%       significantly more internal edges (to vertices of the same        
%       cluster) than external ones (to vertices of another cluster).     
%                                                                         
% There are 10 data sets in the DIMACS10 collection:                      
%                                                                         
% Kronecker:  synthetic graphs from the Graph500 benchmark                
% dyn-frames: frames from a 2D dynamic simulation                         
% Delaunay:   Delaunay triangulations of random points in the plane       
% coauthor:   citation and co-author networks                             
% streets:    real-world street networks                                  
% Walshaw:    Chris Walshaw's graph partitioning archive                  
% matrix:     graphs from the UF collection (not added here)              
% random:     random geometric graphs (random points in the unit square)  
% clustering: real-world graphs commonly used as benchmarks               
% numerical:  graphs from numerical simulation                            
%                                                                         
% Some of the graphs already exist in the UF Collection.  In some cases,  
% the original graph is unsymmetric, with values, whereas the DIMACS      
% graph is the symmetrized pattern of A+A'.  Rather than add duplicate    
% patterns to the UF Collection, a MATLAB script is provided at           
% http://www.cise.ufl.edu/research/sparse/dimacs10 which downloads        
% each matrix from the UF Collection via UFget, and then performs whatever
% operation is required to convert the matrix to the DIMACS graph problem.
% Also posted at that page is a MATLAB code (metis_graph) for reading the 
% DIMACS *.graph files into MATLAB.                                       
%                                                                         
%                                                                         
% Delaunay:  Delaunay Graphs                                              
%                                                                         
% These files have been generated as Delaunay triangulations of random    
% points in the unit square.                                              
%                                                                         
% Engineering a scalable high quality graph partitioner,                  
% M. Holtgrewe, P. Sanders, C. Schulz, IPDPS 2010                         
% http://dx.doi.org/10.1109/IPDPS.2010.5470485                            
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