Online packet routing on linear arrays and rings

Abstract

In contrast to classical offine k-k routing, the online packet routing problem allows for an arbitrary number of packets with arbitrary end points and release times. We study this problem on linear array and ring networks. We generalize an earlier result for the offine problem by showing that Farthest First (FF) scheduling is optimal with respect to makespan on linear arrays. We also show that two other algorithms (Longest in System (LIS) and Moving Priority (MP)) have competitive ratio 2 with respect to makespan on linear arrays. For bidirectional rings, we show that, the competitive ratio of shortest path routing combined with LIS or MP scheduling is in [2:5; 3) and the competitive ratio of shortest path routing combined with FF scheduling is 2. The latter algorithm is optimal among deterministic memoryless algorithms and all algorithms of which we are aware in the literature. © 2011 Springer-Verlag Berlin Heidelberg.