Static and Dynamic Low - Congested Interval
نویسنده
چکیده
Interval Routing Schemes (IRS for short) have been extensively investigated in the past years with special regard to shortest paths. Besides their theoretical interest , IRS have practical applications, as they have been implemented with wormhole routing in the last generation of INMOS Transputer Router Chips. In this paper we consider IRS that are optimal with respect to the congestion of the induced path system. In fact, worm-hole routing is strongly innuenced by the maximum number of paths that share a physical link and from low to moderate congestion it outperforms the packet switching technique. 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 conngurations are xed, and dynamic cases, where they vary over time. All these situations can be handled in a uniied setting, thanks to the notion of competitiveness introduced in this paper. We rst give some general results not related to spe-ciic traac demands. Then, in the one-to-all communication pattern, we show that constructing competitive IRS for a given net-A preliminary version of this paper will appear in the proceedings of the 25th Int. Colloquium on Automata, Languages and Programming (ICALP'98) 4]. work is an intractable problem, both for the static and the dynamic case, that is respectively when the root vertex is xed 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 are 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.
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