Graph Partitioning and Planted Partitions Licentiate thesis, 2008

Graph partitioning is the problem of splitting a graph into two or more partitions of fixed sizes while minimizing the number of edges that are “cut”. This is an important problem with a wide range of applications in fields such as VLSI design, parallel processing, bioinformatics, data mining etc. The planted partition model is a commonly used scheme that defines a certain distribution of graphs; a “planted” partition is used in a way that is likely to make it the unique optimal answer to the partitioning problem. Studying graph partitioning on the planted partition model yields a convenient way of describing the efficiency of an algorithm, i.e. by how often it finds the planted partition. For instance, it is known that if the difference between edge probabilities inside and outside partitions p − r = ­(ln n/n) then the planted partition is the unique optimal answer to the partitioning problem with high probability. We present an algorithm that finds the planted partition with high probability if p − r = ­(n−1/2 ln n). This conveniently describes how well the algorithm works and can often with relative ease be compared to similar results for other algorithms. In this thesis we present two papers. The first paper introduces a simple algorithm with results as mentioned above. In the second paper we discuss the intimately related “inference problem” of finding the planted partition, rather than a solution optimal to the normal graph partitioning problem, as well as similar cases for some other combinatorial problems. Defining and studying a class of such problems is an interesting and open problem to the research community.

planted partition

graph bisection

algorithms

graphs

graph partitioning

clustering

Sal EA, EDIT-huset, Rännvägen 4, Chalmers University of Technology.
Opponent: Prof. Pekka Orponen, Dept. of Information and Computer Science, Helsinki University of Technology TKK, Finland.

Author

Mikael Onsjö

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

A Simple Message Passing Algorithm for Graph Partitioning

Algorithms and Computation 17th International Symposium, ISAAC 2006 Kolkata, India, December 18-20, 2006 Proceedings, Asano, Tetsuo (Ed.),; Vol. 4288(2006)p. 507-516

Paper in proceedings

Finding Most Likely Solutions

Proc. CiE 2007: Computability in Europe,; Vol. 4497(2007)p. 758-767

Paper in proceedings

Subject Categories

Computer Science

Technical report L - Department of Computer Science and Engineering, Chalmers University of Technology and Göteborg University

Sal EA, EDIT-huset, Rännvägen 4, Chalmers University of Technology.

Opponent: Prof. Pekka Orponen, Dept. of Information and Computer Science, Helsinki University of Technology TKK, Finland.