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Geometry, Flows, and Graph-Partitioning Algorithms


Graph partitioning illustration

Figure 1: A graph and a partition into two subsets S, S _ . In this case, the two subsets have equal number of vertices; such a partition is called a bisection. The number of edges crossing the cut is 7. If the number of vertices on the two sides is within a constant factor of each other (say, factor 2), then we call the partition balanced. Balanced partitions are useful in many applications.

"Graph partitioning" refers to a family of computational problems in which the vertices of a graph have to be partitioned into two (or more) large pieces while minimizing the number of the edges that cross the cut. The goal of this paper is to survey an interesting combination of techniques that have recently led to progress on graph partioning problems.

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