| L. Schwiebert, Deadlock-free oblivious wormhole routing with cyclic dependencies, in 9th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA '97), 1997, pp. 149-- 158. |
....as a message of same destination but entering the router by an external input channel, especially when one wants to avoid deadlock using an order on the channels. Therefore, filling up a cycle in D(G;R) is not so easy for input dependent routing function. Actually, it was recently shown in [68] that, as it was suggested in [33] the necessary condition of Dally and Seitz s theorem does not hold: a cycle in a channel dependency graph cannot be easily filled up to obtain a deadlock configuration. This problem holds even for simple definitions of routing functions as input dependent ....
....of wormhole routing, but this does not mean that such a configuration is feasible, i.e. that it can be reached by application of the routing function on some postal sequence. The notion of reachability has already been used by many authors in several different contexts (see for instance [17] and [68]) Let us present this notion in the terminology of our general framework. Let (R; S; H) be any routing function on a graph G, and R 0 be any subfunction of R. Let CD = fc 1 = x 1 ; y 1 ) c 2 = x 2 ; y 2 ) c r = x r ; y r ) c r 1 = c 1 ; r 1g be a cycle in D(G; R; R 0 ) From ....
[Article contains additional citation context not shown here]
L. Schwiebert, Deadlock-free oblivious wormhole routing with cyclic dependencies, in 9th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA '97), 1997, pp. 149-- 158.
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