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This paper establishes the state of the art in both deterministic and randomized online permutation routing in the POPS network. Indeed, we show that any permutation can be routed online on a {\rm POPS}(d, g) network either with O({\frac{d}{g}}\log g) deterministic slots, or, with high probability, with 5c\lceil d/g \rceil + o(d/g) + O(\log\log g) randomized slots, where constant c = \exp (1 + e^{-1}) \approx 3.927. When d = \Theta(g), which we claim to be the "interesting” case, the randomized algorithm is exponentially faster than any other algorithm in the literature, both deterministic and randomized ones. This is true in practice as well. Indeed, experiments show that it outperforms its rivals even starting from as small a network as a POPS(2, 2) and the gap grows exponentially with the size of the network. We can also show that, under proper hypothesis, no deterministic algorithm can asymptotically match its performance.
Optical interconnections, partitioned optical passive star network, permutation routing.
Romeo Rizzi, Alessandro Mei, "Online Permutation Routing in Partitioned Optical Passive Star Networks", IEEE Transactions on Computers, vol. 55, no. , pp. 1557-1571, December 2006, doi:10.1109/TC.2006.202
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