Matrix: DIMACS10/adaptive

Description: DIMACS10 set: numerical/adaptive

DIMACS10/adaptive graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 48 MB. Use UFget(2495) or UFget('DIMACS10/adaptive') in MATLAB.
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    Matrix properties
    number of rows6,815,744
    number of columns6,815,744
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorH. Antz et al.
    editorH. Meyerhenke
    kindundirected graph
    2D/3D problem?no


    10th DIMACS Implementation Challenge:                                    
    As stated on their main website (                                    ), 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        
    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        
        * 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            
        * 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     
        * 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        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.                                        
    numerical: graphs from numerical simulations                             
    For the graphs adaptive and venturiLevel3, please refer to the preprint: 
    Hartwig Anzt, Werner Augustin, Martin Baumann, Hendryk Bockelmann,       
    Thomas Gengenbach, Tobias Hahn, Vincent Heuveline, Eva Ketelaer,         
    Dimitar Lukarski, Andrea Otzen, Sebastian Ritterbusch, Bjo"rn Rocker,    
    Staffan RonnĂ¥s, Michael Schick, Chandramowli Subramanian, Jan-Philipp    
    Weiss, and Florian Wilhelm.  Hiflow3 - a flexible and hardware-aware     
    parallel Finite element package. In Parallel/High-Performance Object-    
    Oriented Scientific Computing (POOSC'10).                                
    For the graphs channel-500x100x100-b050 and packing-500x100x100-b050,    
    please refer to:                                                         
    Markus Wittmann, Thomas Zeiser. Technical Note: Data Structures of       
    ILBDC Lattice Boltzmann Solver.                                     

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    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.