Efficient bufferless packet switching on trees and leveled networks

In bufferless networks the packets cannot be buffered while they are in transit; thus, once injected, the packets have to move constantly. Bufferless networks are interesting because they model optical networks. We consider the tree and leveled network topologies, which represent a wide class of network configurations. On these networks, we study many-to-one batch problems where each node is the source of at most one packet, and the destination of an arbitrary number of packets. Each packet is to follow a preselected path from the source to the destination. Let T ∗ be the optimal delivery time for the packets. We have the following results: • For trees, we present two bufferless algorithms: (i) a deterministic algorithm with delivery time O(δ · T ∗ · log n), and (ii) a randomized algorithm with delivery time O(T ∗ · log n); where, δ is the maximum node degree, and n is the number of nodes. Both algorithms are distributed in the sense that packet forwarding decisions are made locally at the nodes. • For leveled networks, we present two algorithms: (i) a centralized algorithm with delivery time O(T ∗ · log n), and (ii) a distributed algorithm with delivery time O(T ∗ · log n). The first algorithm is centralized in the sense that all decisions are made by a single node. The distributed algorithm simulates the centralized one; the cost of this simulation is an extra logarithmic factor. Our bufferless algorithms are near-optimal, and they improve on previous results for trees and leveled networks by multiple logarithmic factors. ∗This paper is based on two preliminary papers: (1) “Efficient Bufferless Routing on Leveled Networks,” Proceedings of the 11th International Conference on Parallel and Distributed Computing (Euro-par 2005), LNCS 3648, pp 931-940, Lisboa, Portugal, Augoust-September 2005, and (2) “Near-Optimal Hot-Potato Routing on Trees,” Proceedings of the 10th International Conference on Parallel and Distributed Computing (Euro-par 2004), LNCS 3149, pp 820-827, Pisa, Italy, August-September 2004. †Computer Science Department, RPI, 110 8th Street, Troy, NY 12180, USA. Email: [email protected] ‡Computer Science Department, RPI, 110 8th Street, Troy, NY 12180, USA. Email: [email protected] §Computer Science Department, University of Cyprus, P. O. Box 20537, Nicosia CY-1678, Cyprus. Email: [email protected]. projects FLAGS and DELIS.