# A polynomial algorithm for recognizing small cutwidth in hypergraphs

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## Abstract

The Min Cut Linear Arrangment ( Min Cut ) problem for hypergraphs was previously considered by Cahoon and Sahni [CS], where it was called the Board Permutation problem (BP). They gave O(n) and O(n^{3}) algorithms for determining cutwidth 1 and 2, respectively, and cited the open problem: Is there is an algorithm that determines in O(n^{ck}) time if a hypergraph has cutwidth k? We describe an O(n^{m}) algorithm, with m=k^{2}+3K+3, which determines if a hypergraph has cutwidth k. The Min Cut or BP problem, where one wishes to minimize "backplane area" in automating circuit design, is the subject of several recent papers [CS2], [Y], [W], [L], [S], [GCT], [C], [GS].

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