Static and dynamic low-congested interval routing schemes

Abstract

In this paper we consider Interval Routing Schemes (IRS) that are optimal with respect to the congestion of the induced path system. We provide a general framework able to deal with the various congestion issues in IRS. In fact, it is possible to distinguish between static cases, in which the source-destination configurations are fixed, and dynamic cases, where they vary over time. All these situations can be handled in a unified setting, thanks to the notion of competitiveness introduced in this paper. We first give some general results not related to specific traffic demands. Then, in the one-to-all communication pattern, we show that constructing competitive IRS for a given network is an intractable problem, both for the static and the dynamic case, that is respectively when the root vertex is fixed and when it can change along the time. Finally, both for one-to-all and all-to-all communication patterns, we provide nicely competitive k-IRS for relevant topologies. Networks considered arc chains, trees, rings, chordal rings and multi-dimensional grids and tori. We consider both the directed congestion case, in which there are pairwise opposite unidirectional links connecting two neighbor processors, and the undirected congestion case, in which two neighbors are connected by a single bi-directional link.