Packet Routing and Information Gathering in Lines, Rings and Trees

We study the problem of online packet routing and information gathering in lines, rings and trees. A network consists of n nodes. At each node there is a buffer of size B. Each buffer can transmit one packet to the next buffer at each time step. The packets injection is under adversarial control. Packets arriving at a full buffer must be discarded. In information gathering all packets have the same destination. If a packet reaches the destination it is absorbed. The goal is to maximize the number of absorbed packets. Previous studies have shown that even on the line topology this problem is difficult to handle by online algorithms. A lower bound of Ω( √ n) on the competitiveness of the Greedy algorithm was presented by Aiello et al in [2]. All other known algorithms have a polynomial competitive ratio. In this paper we give the first O(log n) competitive deterministic algorithm for the information gathering problem in lines, rings and trees. We also consider multi-destination routing where the destination of a packet may be any node. For lines and rings we show an O(log n) competitive randomized algorithms. Both for information gathering and for the multi-destination routing our results improve exponentially the previous results.