Homework Assignment #3

Due: Tuesday, October 30

Graph Partitioning
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As we discussed in class, there are several practical techniques to
partition graphs based upon the graph type and the optimization
criteria.

Your homework assignment is to analyze several graph partitioning
techniques on several instances representing a variety of graph
classes.

The three input graphs are available from the following ftp site:
ftp://ftp.cc.gatech.edu/pub/people/bader/CSE6140/graph1.gr.gz
ftp://ftp.cc.gatech.edu/pub/people/bader/CSE6140/graph2.gr.gz
ftp://ftp.cc.gatech.edu/pub/people/bader/CSE6140/graph3.gr.gz

- The first graph is the USA Road Network with unit weight edges.
- The second graph is an Erdo"s-Renyi random graph.
- The third graph is a random scale-free graph, using the R-MAT
  generator described in a paper available from
  http://www.siam.org/meetings/sdm04/proceedings/sdm04_043.pdf


Your exercise is to partition each graph into 64 nearly equal-sized
pieces (in terms of vertex count) using k-way graph partitioning,
while minimizing the edgecut.

You should give your answers in a table that, for each row, contains:
 - the graph identifier
 - the graph partitioning software package used
 - the type of partitioning and parameter settings
 - the balance of the output partition
 - the edgecut of the output partition
 - the running time.

Please analyze your results and compare and contrast the methods on
each graph class.

Your homework solution should also provide the details of the computer
used (processor speed, memory, etc.).

Several packages are available for graph partitioning such as METIS
and CHACO. Please use METIS, available from
http://glaros.dtc.umn.edu/gkhome/views/metis

and try several partitioning methods using different matching types
and other parameter settings to figure out the best partitioning.


For extra credit try the following:
1. Try using CHACO or other partitioning packages. CHACO is available from:
http://www.cs.sandia.gov/~bahendr/chaco.html
2. Repeat this same exercise using hypergraph partitioning, such as from hMETiS.