Matrix: DIMACS10/cti

Description: DIMACS10 set: walshaw/cti

DIMACS10/cti graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 179 KB. Use UFget(2521) or UFget('DIMACS10/cti') in MATLAB.
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  • download in Rutherford/Boeing format, file size: 135 KB.

    Matrix properties
    number of rows16,840
    number of columns16,840
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorC. Walshaw
    editorC. Walshaw
    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.                                       
    Walshaw:  Chris Walshaw's graph partitioning archive                    
    Chris Walshaw's graph partitioning archive contains 34 graphs that      
    have been very popular as benchmarks for graph partitioning algorithms  
    ( ).                     
    17 of them are already in the UF Collection.  Only the 17 new graphs    
    not yet in the collection are added here in the DIMACS10 set.           
    DIMACS10 graph:                 new?   UF matrix:                       
    ---------------                 ----   -------------                    
    walshaw/144                      *     DIMACS10/144                     
    walshaw/3elt                           AG-Monien/3elt                   
    walshaw/4elt                           Pothen/barth5                    
    walshaw/598a                     *     DIMACS10/598a                    
    walshaw/add20                          Hamm/add20                       
    walshaw/add32                          Hamm/add32                       
    walshaw/auto                     *     DIMACS10/auto                    
    walshaw/bcsstk29                       HB/bcsstk29                      
    walshaw/bcsstk30                       HB/bcsstk30                      
    walshaw/bcsstk31                       HB/bcsstk31                      
    walshaw/bcsstk32                       HB/bcsstk32                      
    walshaw/bcsstk33                       HB/bcsstk33                      
    walshaw/brack2                         AG-Monien/brack2                 
    walshaw/crack                          AG-Monient/crack                 
    walshaw/cs4                      *     DIMACS10/cs4                     
    walshaw/cti                      *     DIMACS10/cti                     
    walshaw/data                     *     DIMACS10/data                    
    walshaw/fe_4elt2                 *     DIMACS10/fe_4elt2                
    walshaw/fe_body                  *     DIMACS10/fe_body                 
    walshaw/fe_ocean                 *     DIMACS10/fe_ocean                
    walshaw/fe_pwt                         Pothen/pwt                       
    walshaw/fe_rotor                 *     DIMACS10/fe_rotor                
    walshaw/fe_sphere                *     DIMACS10/fe_sphere               
    walshaw/fe_tooth                 *     DIMACS10/fe_tooth                
    walshaw/finan512                       Mulvey/finan512                  
    walshaw/m14b                     *     DIMACS10/m14b                    
    walshaw/memplus                        Hamm/memplus                     
    walshaw/t60k                     *     DIMACS10/t60k                    
    walshaw/uk                       *     DIMACS10/uk                      
    walshaw/vibrobox                       Cote/vibrobox                    
    walshaw/wave                           AG-Monien/wave                   
    walshaw/whitaker3                      AG-Monien/whitaker3              
    walshaw/wing                     *     DIMACS10/wing                    
    walshaw/wing_nodal               *     DIMACS10/wing_nodal              

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    DIMACS10/cti svd

    For a description of the statistics displayed above, click here.

    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.