Asymmetric sparse telescope

Constructions of Sparse Asymmetric Connectors

We consider the problem of connecting a set I of n inputs to a set O of N outputs (n ≤ N) by as few edges as possible, such that for each injective mapping f : I → O there are n vertex disjoint paths from i to f(i) of length k for a given k ∈ N. For k = Ω(logN + log n) Oruç [5] gave the presently best (n,N)-connector with O(N +n · log n) edges. For k = 2 we show by a probabilistic argument that...

An Explicit Construction of Sparse Asymmetric Connectors

An (N,K, `) connector (rearrangeable network) is a digraph with N inputs and K outputs such that for any injective mapping from the outputs to the inputs there is a set of vertex disjoint paths of length ` implementing it. The study of this problem begins with the pioneering work of Shannon, Slepian, Clos and Beneš in the 1950’s who studied the balanced N = K case, and arbitrary depth `, and la...

Sparse Asymmetric Connectors in Communication Networks

An (n,N, d)–connector is an acyclic digraph with n inputs and N outputs in which for any injective mapping of input vertices into output vertices there exist n vertex disjoint paths of length d joining each input to its corresponding output. We consider the problem of construction of sparse (n,N, 2)–connectors (depth 2 connectors) when n N . The probabilistic argument in [1] shows the existence...

Predicting Complex Behavior in Sparse Asymmetric Networks

Recurrent networks of threshold elements have been studied intensively as associative memories and pattern-recognition devices. While most research has concentrated on fully-connected symmetric networks. which relax to stable fixed points. asymmetric networks show richer dynamical behavior. and can be used as sequence generators or flexible pattern-recognition devices. In this paper. we approac...

Source Telescope Source Telescope