Distributed Queuing in Dynamic Networks

We consider the problem of forming a distributed queue in the adversarial dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. This is a synchronous model in which network nodes are assumed to be fixed, the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors are for the current round before they broadcast their messages. Queue requests may arrive over rounds at arbitrary nodes and the goal is to eventually enqueue them in a distributed queue. We present two algorithms that give a total distributed ordering of queue requests in this model. We measure the performance of our algorithms through round complexity, which is the total number of rounds needed to solve the distributed queuing problem. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in O(nk) rounds using O(log n) size messages, where n is the number of nodes in the network and k <= n is the number of queue requests. Further, we show that for more stable graphs, e.g. T-interval connected graphs where the communication links change in every T rounds, the distributed queuing problem can be solved in O(n+ (nk/min(alpha,T))) rounds using the same O(log n) size messages, where alpha > 0 is the concurrency level parameter that captures the minimum number of active queue requests in the system in any round. These results hold in any arbitrary (sequential, one-shot concurrent, or dynamic) arrival of k queue requests in the system. Moreover, our algorithms ensure correctness in the sense that each queue request is eventually enqueued in the distributed queue after it is issued and each queue request is enqueued exactly once. We also provide an impossibility result for this distributed queuing problem in this model. To the best of our knowledge, these are the first solutions to the distributed queuing problem in adversarial dynamic networks.Comment: In Proceedings FOMC 2013, arXiv:1310.459

An Inherent Bottleneck in Distributed Counting

A distributed counter allows each processor in an asynchronous message passing network to access the counter value and increment it. We study the problem of implementing a distributed counter such that no processor is a communication bottleneck. We prove a lower bound of\Omega\Gamma/20 n= log log n) on the number of messages that some processor must exchange in a sequence of n counting operations spread over n processors. We propose a counter that achieves this bound when each processor increments the counter exactly once. Hence, the lower bound is tight. Because most algorithms and data structures count in some way, the lower bound holds for many distributed computations. We feel that the proposed concept of a communication bottleneck is a relevant measure of efficiency for a distributed algorithm and data structure, because it indicates the achievable degree of distribution. 1 Introduction Counting is an essential ingredient in virtually any computation. It is therefore highly de..