Packet Routing and Information Gathering in Lines, Rings and Trees

Abstract

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 2 n) competitive randomized algorithms. Both for information gathering and for the multi-destination routing our results improve exponentially the previous results.

An O(logn)-Competitive Online Centralized Randomized Packet-Routing Algorithm for Lines

“…In [AKOR03], a lower bound of Ω( √ n) was proved for the greedy algorithm on directed lines if the buffer size B is at least two. For the case B = 1 (in a slightly different model), an Ω(n) lower bound for any deterministic algorithm was proved by [AZ05,AKK09]. Both [AZ05] and [AKK09] developed, among other things, online randomized centralized algorithms for directed paths with B > 1.…”

“…For the case B = 1 (in a slightly different model), an Ω(n) lower bound for any deterministic algorithm was proved by [AZ05,AKK09]. Both [AZ05] and [AKK09] developed, among other things, online randomized centralized algorithms for directed paths with B > 1. In [AKK09] an O(log 3 n)-competitive algorithm was presented if the buffer size B is at least 2.…”

“…For the case B = 1, they presented a randomizedÕ( √ n)-competitive distributed algorithm. In [AZ05], an O(log 2 n)-competitive algorithm was presented for the case B ≥ 2. This algorithm may work also with a FIFO policy for managing the buffers.…”

“…(II) Our algorithm works also for buffers of size B = 1. (III) We consider also the parameter c of the capacity of the links ( [AZ05,AKK09] considered only the case c = 1).…”

“…Following [AAF96, ARSU02, AZ05, RR09], we apply a space-time transformation to reduce the problem of packet routing to path packing problem. Unlike [AZ05], we do not consider fractional online multi-commodity flows. Instead, we apply the primal-dual framework of [BN06] to obtain an integral packing of paths.…”