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EVOLVING MULTI-LEVEL GRAPH
PARTITIONING ALGORITHMS
Master : Ali Jahanian
Student : Mohammad
Rostami
Introduction
Graph Partitioning
Evolutionary
Computation
Genetic
Programming
Review
Primitive
Operation Set
Experiment
Results
Conclusion
Future Work
 organizing parallel computation
workload
VLSI layout design
image processing
critical infrastructure protection
optimal graph partitioning is known to
be NP-hard
Introduction
Graph Partitioning
 The total weight for a set of vertices X is given by:
the total weight of a set of edges Y is:
A balanced partition requires that:
Graph Partitioning
Coarsening:
 Random matching
 Light edge matching
 Heavy edge matching
Partition
 Graph growing partition (GGP)
 Greedy graph growing partition (GGGP)
Multi-level Graph Partitioning
Uncoarsening and Refinement:
 KL refinement
 Greedy refinement
Multi-level Graph Partitioning
Initialization
Parent selection
Recombination
Mutation
Survival selection
Termination
Evolutionary Computation
Evolutionary Computation
Methodology
Methodology
Primitive Operation Set
Erdos-R ¨ enyi
Barab ´ asi- ´ Albert
Los Alamos National Laboratory (LANL)
One month of the network data set was modeled
as a bipartite graph with 9,924 user vertices,
14,822 computer vertices, and 106,693
authentication edges. Subgraphs were created by
inducing the set of vertices visited by a random
walk of the total graph.
Experiment
Results
Results
Results
Results
Although there are a variety of multi-level
partitioning algorithms available, most are
intended to serve as general purpose solutions.
An obvious continuation of this work would be to
include the consideration of execution time.
Instead of focusing on reducing the cost of the
partitions produced, evolved partitioners could
instead aim to reduce the time needed to partition
certain types of graphs for time-sensitive
applications.
Conclusion & Future Work
Question ?

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Evolving multi level graph