Universal bufferless routing

Abstract

Given an arbitrary network, and a routing problem with congestion C and dilation D, a long standing open problem is to show the existence of bufferless routing algorithms with optimal performance guarantees (routing time close to the lower bound Ω(C+D)). Our main result is a new deterministic technique that constructs a universal bufferless algorithm by emulating a universal buffered algorithm. The heart of the emulation is to replace packet buffering with packet circulation on regions of the network. The cost of the emulation on the routing time is proportional to the square of the node buffer size used by the buffered algorithm. We apply this emulation to a simple randomized buffered algorithm to obtain a distributed, universal bufferless algorithm with routing time O((C + D) · log3(n + N)), which is within poly-logarithmic factors from the optimal, where n is the size of the network and N is the number of packets. The bufferless competitive ratio is the ratio of the best achievable bufferless routing time, to the best achievable buffered routing time. We give the first non-trivial bound of O(log3(n + N)) for the bufferless competitive ratio for arbitrary routing problems. © Springer-Verlag Berlin Heidelberg 2005.