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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.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Tom Leighton, Fillia Makedon, and Spyros Tragoudas, "Hypergraph Partitioning Algorithms." Dartmouth Computer Science Technical Report PCS-TR94-233, October, 1994.
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