R. Cypher, STORAGE-EFFICIENT, DEADLOCK-FREE PACKET ROUTING ALGORITHMS FOR TORUS NETWORKS, I.E.E.E. transactions on computers, 43(12), 1994, pp. 1376-1385
We present two new packet routing algorithms for parallel computers wi
th torus interconnection networks of arbitrary size and dimension, Bot
h algorithms use only minimal length paths, are fully adaptive in the
sense that all minimal length paths may be used to avoid congestion, a
nd are free of deadlock, livelock and starvation. Algorithm 1 requires
only three central queues per routing node, It is the first known min
imal length packet routing algorithm for torus networks which requires
a constant number of queues per node, regardless of the size and dime
nsion of the torus, In fact, the requirement of three queues per node
is optimal, as no such algorithm is possible when all nodes have two o
r fewer queues. Algorithm 2 requires only that each node have two inpu
t buffers per edge, It is the first known minimal-fully-adaptive packe
t routing algorithm for torus networks which does not require central
queues and which does not require any node to have more than two input
or two output buffers per edge. Both algorithms are simple and appear
to be well-suited to VLSI implementation, They can be used with eithe
r store-and-forward or virtual cut-through routing,