Online Permutation Routing in Partitioned Optical Passive Star Networks

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 POPS 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 $d=\Theta(g)$, that 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

The VLSI Optimality of the AKS Sorting Network

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424IBM Predoctoral Fellowship Progra

Smallest Compact Formulation for the Permutahedron

In this note, we consider the permutahedron, the convex hull of all permutations of {1,2…,n} . We show how to obtain an extended formulation for this polytope from any sorting network. By using the optimal Ajtai–Komlós–Szemerédi sorting network, this extended formulation has Θ(nlogn) variables and inequalities. Furthermore, from basic polyhedral arguments, we show that this is best possible (up to a multiplicative constant) since any extended formulation has at least Ω(nlogn) inequalities. The results easily extend to the generalized permutahedron.National Science Foundation (U.S.) (Contract CCF-0829878)National Science Foundation (U.S.) (Contract CCF-1115849)United States. Office of Naval Research (Grant 0014-05-1-0148