Istituto di Scienza e Tecnologie dell'Informazione     
Martelli A., Preparata F. On thickness and cascade decomposition of permutation connections. Internal note IEI-B69-19, 1969.
In the class of interconnection networks, this paper analyze some problems regarding permutation connections, i.e. the set of n links realizing the mapping of an n-terminal array into an n-terminal array. A first problem is the partition of the connection links into the least number (thickness) of sets of mutually noncrossing links (layers) and a simple algorithm is offered for its solution. A second problem is the realization of a connection as a cascade of two-layers connections (stages): lower- and upper-bounds are given for the number of stages and constructive procedure are implicity offered. Finally, the permutations of degree n are enumerated according to their thickness.
Subject Permutation connections
Cascade decomposition

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