Constructions of Sparse Asymmetric Connectors with Number Theoretic Methods
2005 (English)In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 45, no 3, 119-124 p.Article in journal (Refereed) Published
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 every injective mapping f : I → O there are n vertex disjoint paths from i to f(i) of length k for a given k . For k = Ω(log N + logn) Oruς (1994) gave the presently best (n,N)-connector with O(N+n·log n) edges. For k=2 and N the square of a prime, Richards and Hwang (1985) described a construction using edges. We show by a probabilistic argument that an optimal (n,N)-connector has Θ (N) edges, if for some ε>0. Moreover, we give explicit constructions based on a new number theoretic approach that need at most edges for arbitrary choices of n and N. The improvement we achieve is based on applying a generalization of the Erdös-Heilbronn conjecture on the size of restricted sums.
Place, publisher, year, edition, pages
John Wiley & Sons, 2005. Vol. 45, no 3, 119-124 p.
connector, rearrangeable network, sparse switch, permuter, combinatorial number theory, restricted sums
IdentifiersURN: urn:nbn:se:umu:diva-83129DOI: 10.1002/net.20058OAI: oai:DiVA.org:umu-83129DiVA: diva2:665017