Randomized algorithms
How much can hardware help routing?
Journal of the ACM (JACM)
Realizing Common Communication Patterns in Partitioned Optical Passive Stars (POPS) Networks
IEEE Transactions on Computers
Matrix Multiplication and Data Routing Using a Partitioned Optical Passive Stars Network
IEEE Transactions on Parallel and Distributed Systems
The Partitioned Optical Passive Stars Network: Simulations and Fundamental Operations
IEEE Transactions on Parallel and Distributed Systems
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
Optimal hypercube simulation on the partitioned optical passive stars network
The Journal of Supercomputing
| Hi-index | 14.98 |
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.