Selection networks with 8n log2n size and O(log n) depth
An (n,n/2)-selector is a comparator network that classifies a set of n values into two classes with the same number of values in such a way that each element in one class is at least as large as all of those in the other. Based on utilization of expanders, Pippenger constructed (n,n/2)-selectors, whose size is asymptotic to 2nlog2n and whose depth is O((log n)2). In the same spirit, we obtain a relatively simple method to construct (n,n/2)-selectors of depth O(log n). We construct (n,n/2)-selectors of size at most 8n log2n + O(n). Moreover, for arbitrary C>3/log23=1.8927 ..., we construct (n,n/2)-selectors of size at most Cnlog2n+O(n).
KeywordsPositive Integer Total Size Selection Network Output Terminal Optimal Switching
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