On the Number of Permutations Performable by the Augmented Data Manipulator Network

Fast permutation routing in a class of interconnection networks

“…The correctness and timing of the routing algorithm hinge on the fundamental properties of ADM networks summarized in Lemmas 2.1 and 2.2 below. The result in Lemma 2.1 was first mentioned in [2] and used subsequently in [1,7,8]. Properties equivalent to Lemma 2.2 were also used in [1,7,8].…”

“…The result in Lemma 2.1 was first mentioned in [2] and used subsequently in [1,7,8]. Properties equivalent to Lemma 2.2 were also used in [1,7,8]. For our purpose, however, we use graph-theoretic concepts to present and prove the properties.…”

“…Several mathematical aspects of ADMs have been examined in the literature: First, the problem of determining the exact permutation power of ADM networks (i.e., counting the number of admissible permutations) was initiated in [1] and [11]. Later, Leland [8] (see also [9]) showed a set of recurrence relations for the exact number P(N) of ADM admissible permutations.…”

A universal performance factor for multi-criteria evaluation of multistage interconnection networks

“…Several MIN architectures were proposed in the literature [32,38] and a lot of work was devoted to study, evaluate and compare their performance [2,39]. Multi-criteria MIN performance evaluation is not easy to be established because of the large number of factors to be evaluated and their software and hardware dependencies [27].…”