A packet routing protocol for arbitrary networks

Abstract

In this paper, we introduce an on-line protocol which routes any set of packets along shortest paths through an arbitrary N-node network in O(congestion + diameter + log N) rounds, with high probability. This time bound is optimal up to the additive log N, and it was previously only reached for bounded-degree levelled networks. Further, we prove bounds on the congestion of random routing problems for Cayley networks and general node symmetric networks based on the construction of shortest paths systems. In particular, we give construction schemes for shortest paths systems and show that if every processor sends p packets to random destinations along the paths described in the paths system, then the congestion is bounded by O(p. diameter + log N), with high probability. Finally, we prove an (apparently suboptimal) congestion bound for random routing problems on randomly chosen regular networks.