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Abstract: We present the first polynomial time approximation algorithms for the balanced hypergraph partitioning problem. The approximations are within polylogarithmic factors of the optimal solutions. The choice of algorithm involves a time complexity/approximation bound tradeoff. We employ a two step methodology. First we approximate the flux of the input hypergraph. This involves an approximate solution to a concurrent flow problem on the hypergraph. In the second step we use the approximate flux to obtain approximations for the balanced bipartitioning problem. Our results extend the approximation algorithms by Leighton-Rao on graphs to hypergraphs. We also give the first polylogarithmic times optimal approximation algorithms for multiway (graph and hypergraph) partitioning problems into bounded size sets. A better approximation algorithm for the latter problem is finally presented for the special case of bounded sets of size at most O(log n) on planar graphs and hypergraphs, where n is the number of nodes of the input instance.

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   Tom Leighton, Fillia Makedon, and Spyros Tragoudas, "Hypergraph Partitioning Algorithms." Dartmouth Computer Science Technical Report PCS-TR94-233, October, 1994.

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