DIMACS10 set: walshaw/wing_nodal
Name wing_nodal
Group DIMACS10
Matrix ID 2533
Num Rows 10,937
Num Cols 10,937
Nonzeros 150,976
Pattern Entries 150,976
Kind Undirected Graph
Symmetric Yes
Date 2000
Author C. Walshaw
Editor C. Walshaw
Structural Rank
Structural Rank Full
Num Dmperm Blocks
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate no
Positive Definite no
Type binary
SVD Statistics
Matrix Norm 1.505510e+01
Minimum Singular Value 6.396824e-06
Condition Number 2.353527e+06
Rank 10,937
Null Space Dimension 0
Full Numerical Rank? yes
Download Singular Values MATLAB
Download MATLAB Rutherford Boeing Matrix Market
10th DIMACS Implementation Challenge:                                   
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       
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           
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.                                       
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  
( http://staffweb.cms.gre.ac.uk/~wc06/partition/ ).                     
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