Minimal Adaptive Routing on the Mesh with Bounded Queue Size

An O(N) Oblivious Routing Algorithm for Two-Dimensional Meshes of Constant Queue-Size

“…The first idea (i) also appears in [4,7]: Let us take a look at the above example again. At the first step, the leftmost packet d 1 moves to the right and P 1 now holds a 1 and d 1 .…”

“…If a null packet exists at a processor P i , then P i 's queue is just empty. Namely, PAD 4 x is defined to be…”

“…However, these algorithms involve a flavor of mesh-sorting algorithms and may be too complicated to implement on existing computers. If adaptive algorithms are limited to simpler ones, i.e., minimal, destinationexchangeable, and constant queue-size, then a lower bound jumps up to N as proven by Chinn et al [4]. An oblivious path selection is another well-received approach [2,3,9].…”

A Lower Bound for Elementary Oblivious Routing on Three-Dimensional Meshes

“…However, this is clearly not accepted as a practical answer (and that is why so many studies have been done for deterministic oblivious routing). Another possibility is adding a small amount of adaptiveness to the oblivious condition, like the dimension-exchange approach [1,5]. Unfortunately, we cannot hope too much either since a quite high lower bound has been proved for 2D meshes [5].…”

A Lower Bound for Nearly Minimal Adaptive and Hot Potato Algorithms

“…Chinn et al [10] give a nontrivial lower bound on the time it takes to route so-called permutation routing problems for algorithms that require packets to take shortest (or minimal) paths to their destination and use a bounded amount of buffer space. There are many algorithms that route arbitrary permutations in O(n) steps on the synchronous n × n mesh (see [10] for a list), but for one or more reasons none would be implemented in practice. One reason is that these asymptotically optimal algorithms require complex decisions to route the packets-too complex to be practical.…”