Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A high-level framework for distributed processing of large-scale graphs
ICDCN'11 Proceedings of the 12th international conference on Distributed computing and networking
HipG: parallel processing of large-scale graphs
ACM SIGOPS Operating Systems Review
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A bisection of a graph with $n$ vertices is a partition of its vertices into two sets, each of size $n/2$. The bisection cost is the number of edges connecting the two sets. The problem of finding a bisection of minimum cost is prototypical to graph partitioning problems, which arise in numerous contexts. This problem is NP-hard. We present an algorithm that finds a bisection whose cost is within a factor of $O(\log^{1.5} n)$ from the minimum. For graphs excluding any fixed graph as a minor (e.g., planar graphs) we obtain an improved approximation ratio of $O(\log n)$. The previously known approximation ratio for bisection was roughly $\sqrt{n}$.