Optimal mapping of neighbourhood-constrained systems
The problem of finding the minimum topology of multiprocessing substrates supporting parallel execution of any given neighbourhood-constrained system is proposed and possible optimal strategies are investigated based on the relationship between Barbosa's scheduling by edge reversal — SER — distributed algorithm and the minimum clique covering problem. It is shown that from any given clique covering of length λ on a graph G, it is possible to obtain a SER trailer dynamics in G's complement that cover G upon λ evolutions. It also shown that, conversely, from any given SER dynamics on G in which all of its nodes operate at least once upon λ steps, a clique covering of length at most λ is defined on G's complement. In addition, a conjecture correlating the length of any minimum clique covering and optimal concurrency in SER- driven systems is stablished.
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