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

Dynamic Analysis of the Arrow Distributed Protocol

Distributed queuing is a fundamental coordination problem that arises in a variety of applications, including distributed directories, totally ordered multicast, and distributed mutual exclusion. The arrow protocol is a solution to distributed queuing that is based on path reversal on a pre-selected spanning tree of the network. We present a novel and comprehensive competitive analysis of the arrow protocol. We consider the total cost of handling a finite number of queuing requests, which may or may not be issued concurrently, and show that the arrow protocol is $O(s\cdot \log D)$ -competitive to the optimal queuing protocol, where s and D are the stretch and the diameter, respectively, of the spanning tree. In addition, we show that our analysis is almost tight by proving that for every spanning tree chosen for execution, the arrow protocol is $\Omega(s \cdot \log(D/s)/{\log}\log(D/s))$ -competitive to the optimal queuing protocol. Our analysis reveals an intriguing connection between the arrow protocol and the nearest neighbor traveling salesperson tour on an appropriately defined grap

Analysis of an Efficient Distributed Algorithm for Mutual Exclusion (Average-Case Analysis of Path Reversal)

The algorithm analysed by Naïmi, Trehe and Arnold was the very first distributed algorithm to solve the mutual exclusion problem in complete networks by using a dynamic logical tree structure as its basic distributed data structure, viz. a path reversal transformation in rooted n-node trees; besides, it was also the first one to achieve a logarithmic average-case message complexity. The present paper proposes a direct and general approach to compute the moments of the cost of path reversal. It basically uses one-one correspondences between combinatorial structures and the associated probability generating functions: the expected cost of path reversal is thus proved to be exactly $H_{n-1}$. Moreover, time and message complexity of the algorithm as well as randomized bounds on its worst-case message complexity in arbitrary networks are also given. The average-case analysis of path reversal and the analysis of this distributed algorithm for mutual exclusion are thus fully completed in the paper. The general techniques used should also prove available and fruitful when adapted to the most efficient recent tree-based distributed algorithms for mutual exclusion which require powerful tools, particularly for average-case analyses

Exclusion and Object Tracking in a Network of Processes

This paper concerns two fundamental problems in distributed computing---mutual exclusion and mobile object tracking. For a variant of the mutual exclusion problem where the network topology is taken into account, all existing distributed solutions make use of tokens. It turns out that these token-based solutions for mutual exclusion can also be adapted for object tracking, as the token behaves very much like a mobile object. To handle objects with replication, we go further to consider the more general $k$-exclusion problem which has not been as well studied in a network setting. A strong fairness property for $k$-exclusion requires that a process trying to enter the critical section will eventually succeed even if \emph{up to} $k-1$ processes stay in the critical section indefinitely. We present a comparative survey of existing token-based mutual exclusion algorithms, which have provided much inspiration for later $k$-exclusion algorithms. We then propose two solutions to the $k$-exclusion problem, the second of which meets the strong fairness requirement. Fault-tolerance issues are also discussed along with the suggestion of a third algorithm that is also strongly fair. Performances of the three algorithms are compared by simulation. Finally, we show how the various exclusion algorithms can be adapted for tracking mobile objects

Concurrent Distributed Serving with Mobile Servers

This paper introduces a new resource allocation problem in distributed computing called distributed serving with mobile servers (DSMS). In DSMS, there are k identical mobile servers residing at the processors of a network. At arbitrary points of time, any subset of processors can invoke one or more requests. To serve a request, one of the servers must move to the processor that invoked the request. Resource allocation is performed in a distributed manner since only the processor that invoked the request initially knows about it. All processors cooperate by passing messages to achieve correct resource allocation. They do this with the goal to minimize the communication cost. Routing servers in large-scale distributed systems requires a scalable location service. We introduce the distributed protocol Gnn that solves the DSMS problem on overlay trees. We prove that Gnn is starvation-free and correctly integrates locating the servers and synchronizing the concurrent access to servers despite asynchrony, even when the requests are invoked over time. Further, we analyze Gnn for "one-shot" executions, i.e., all requests are invoked simultaneously. We prove that when running Gnn on top of a special family of tree topologies - known as hierarchically well-separated trees (HSTs) - we obtain a randomized distributed protocol with an expected competitive ratio of O(log n) on general network topologies with n processors. From a technical point of view, our main result is that Gnn optimally solves the DSMS problem on HSTs for one-shot executions, even if communication is asynchronous. Further, we present a lower bound of Omega(max {k, log n/log log n}) on the competitive ratio for DSMS. The lower bound even holds when communication is synchronous and requests are invoked sequentially

Quantization for Secret Key Generation in Underwater Acoustic Channels

openSecuring wireless communications in harsh environments, such as underwater networks, via traditional cryptographic approaches is unfeasible. For example, public key encryption would require a public key infrastructure and a key management infrastructure. A viable solution is instead physical layer security, allowing two devices to obtain a symmetric cryptographic key from the randomness provided by the underlying communication channel, which varies in time, frequency, and space, in general. The probability of having both parties generating the same key and its number of bits greatly depend on how sampled observations are quantized. In this thesis, novel data-driven quantization techniques, which make use of specific channel features computed from impulse responses collected from real experiments, are investigated. In particular, we propose a new machine learning algorithm that quantizes an input vector into an initial key, as close as possible to a series of independent and uniformly distributed symbols and matches at beast the corresponding initial key of the corresponding receiver, to guarantee a high key agreement probability and to avoid an eavesdropper to infer future values exploiting the correlation between consecutive symbols. We also propose an adversarial neural network architecture, where legitimate parties feature a neural quantizer to produce the initial key, whereas the eavesdropper tries to reconstruct the key agreed by the first two

Graphical Simulation Tool from Logical Token-based Distributed Mutual Exclusion Algorithms�

Computer Science