Online Permutation Routing in Partitioned Optical Passive Star Networks

TL;DR

This paper presents new deterministic and randomized algorithms for online permutation routing in POPS networks, demonstrating significant improvements in efficiency, especially in the case where network parameters are balanced, supported by theoretical analysis and experimental results.

Contribution

It introduces faster randomized routing algorithms for POPS networks and proves their asymptotic optimality compared to deterministic methods.

Findings

Randomized routing outperforms deterministic algorithms in speed.

The proposed algorithms are effective even on small networks.

Experimental results confirm exponential performance gains with network size.

Abstract

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.