Size Bounds for Superconcentrators

Abstract We prove that any N-superconcentrator of indegree two has at least 4N - o(N) nodes. From this lower bounds of 4N - o(N) follow on the number of additions required to compute the Discrete Fourier Transform of prime order and cyclic convolution. Using small examples we illustrate how small superconcentrators can suggest fast algorithms for instances of these problems. For superconcentrators with no degree restrictions we prove a lower bound of 5N - o(N) edges. Also, we give a recursive construction with 3N log2 N edges that improves on the best bounds previously known for values of N up to several thousand.

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