Issue No. 05 - May (2008 vol. 57)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.23
In the oblivious path selection problem, each packet in the network independently chooses a path, which is an important property if the routing algorithm is to be independent of the traffic distribution. The quality of the paths is determined by the congestion $C$, the maximum number of paths crossing an edge, and the dilation $D$, the maximum path length. So far, the oblivious algorithms studied in the literature have focused on minimizing the congestion while ignoring the dilation. An open question is whether $C$ and $D$ can be controlled simultaneously. Here, we answer this question for the $d$-dimensional mesh. We present an oblivious algorithm for which $C$ and $D$ are both within $O(d^2)$ of optimal. The algorithm uses randomization, and we show that the number of random bits required per packet is within $O(d)$ of the minimum number of random bits required by any algorithm that obtains the same congestion. For fixed $d$, our algorithm is asymptotically optimal.
C. Busch, J. Xi and M. Magdon-Ismail, "Optimal Oblivious Path Selection on the Mesh," in IEEE Transactions on Computers, vol. 57, no. , pp. 660-671, 2008.