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<p><b>Abstract</b>—The <it>minimum-congestion hypergraph embedding in a cycle (MCHEC)</it> problem is to embed the <it>n</it> edges in an <it>m</it>-vertex hypergraph as paths in a cycle on the same number of vertices, such that <it>congestion</it>—the maximum number of paths that use any single edge in the cycle—is minimized. The MCHEC problem has applications in electronic design automation and parallel computing. In this paper, it is proven that the MCHEC problem is NP-complete. An <it>O</it>((<it>nm</it>)<super><it>k</it>+1</super>) algorithm is described that computes an embedding with congestion <it>k</it> or determines that such an embedding does not exist. Finally, a linear-time approximation algorithm for arbitrary instances is presented that computes an embedding whose congestion is at most three times optimal.</p>
Hypergraph embedding in a cycle, congestion, NP-completeness, approximation algorithms, routing around a rectangle, moat routing, ring routing.

J. P. Cohoon and J. L. Ganley, "Minimum-Congestion Hypergraph Embedding in a Cycle," in IEEE Transactions on Computers, vol. 46, no. , pp. 600-602, 1997.
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