Embedding one Interconnection Network in Another

Improved Compressions of Cube-Connected Cycles Networks

“…Most of the work was done on one-to-one embeddings (for an overview, see e.g. 25,29]), but results on many-to-one embeddings can also be found (see e.g. 2,6,7,9,12,13,16,18,22,26,27]).…”

“…Much of the work has been focused on the capability of certain networks to simulate other network or algorithm structures, in order to execute parallel algorithms of a special structure e ciently on di erent processor networks (see e.g. 5,17,25]). One problem that is of speci c interest in this context is that many existing algorithms are designed for arbitrarily large networks (see e.g.…”

Complexity: A Language-Theoretic Point of View

“…To built parallel architectures whose communication structure has high communication facilities is one of the central tasks of parallel computing. There are many studies in this direction dealing with the efficiency of the realization of basic communication tasks (like broadcast, gossip [91], routing [102]) in distinct communication structures as well as with the ability to effective simulate the communication facilities of several different interconnection networks (communication structures) on one network candidating for our parallel architecture [112]. Results and methods used in this area are primary connected with discrete mathematics and graph theory [102,112] and so we do not want to give more details here.…”

“…There are many studies in this direction dealing with the efficiency of the realization of basic communication tasks (like broadcast, gossip [91], routing [102]) in distinct communication structures as well as with the ability to effective simulate the communication facilities of several different interconnection networks (communication structures) on one network candidating for our parallel architecture [112]. Results and methods used in this area are primary connected with discrete mathematics and graph theory [102,112] and so we do not want to give more details here. We omit to discuss typical parallel models of formal language theory like systolic arrays, Lindenmayer systems and other kinds of parallel rewriting too because they are not in any main research streams in the complexity of parallel computing.…”

Congestion optimale du plongement de l’hypercube $H (n)$ dans la chaîne $P(2^n)$

“…La théorie du plongement des graphes a pris une grande importance ces dernières années (pour un résumé, voir [11,12]). Parmi les applications de la théorie des plongements, il y a l'émulation d'une architecture par une autre architecture d'une manière efficace (la possibilité pour un réseau d'interconnexion de pouvoir simuler efficacement un programme écrit pour une autre architecture).…”