In this work we consider the problem of gathering autonomous robots in the plane. In particular, we consider non-transparent unit-disc robots (i.e., fat) in an asynchronous setting. Vision is the only mean of coordination. Using a state-machine representation we formulate the gathering problem and develop a distributed algorithm that solves the problem for any number of robots.The main idea behind our algorithm is for the robots to reach a configuration in which all the following hold: (a) The robots' centers form a convex hull in which all robots are on the convex, (b) Each robot can see all other robots, and (c) The configuration is connected, that is, every robot touches another robot and all robots together form a connected formation. We show that starting from any initial configuration, the robots, making only local decisions and coordinate by vision, eventually reach such a configuration and terminate, yielding a solution to the gathering problem.

Citation for the published paper: Dolev, S. ; Georgiou, C. ; Marcoullis, I. et al. (2015) Abstract. Virtual synchrony (VS) is an important abstraction that is proven to be extremely useful when implemented over asynchronous, typically large, message-passing distributed systems. Fault tolerant design is critical for the success of such implementations since large distributed systems can be highly available as long as they do not depend on the full operational status of every system participant. Self-stabilizing systems can tolerate transient faults that drive the system to an arbitrary unpredictable configuration. Such systems automatically regain consistency from any such configuration, and then produce the desired system behavior ensuring it for practically infinite number of successive steps, e.g., 2 64 steps. We present a new multi-purpose self-stabilizing counter algorithm establishing an efficient practically unbounded counter, that can directly yield a self-stabilizing Multiple-Writer Multiple-Reader (MWMR) register emulation. We use our counter algorithm, together with a selfstabilizing group membership and a self-stabilizing multicast service to devise the first practically stabilizing VS algorithm and a self-stabilizing VS-based emulation of state machine replication (SMR). As we base the SMR implementation on VS, rather than consensus, the system progresses in more extreme asynchronous settings in relation to consensusbased SMR.

This paper investigates time-efficient implementations of atomic read-write registers in message-passing systems where the number of readers can be unbounded. In particular we study the case of a single writer, multiple readers, and S servers, such that the writer, any subset of the readers, and up to t servers may crash. A recent result of Dutta et al. [3] shows how to obtain fast implementations in which both reads and writes complete in one communication round-trip, under the constraint that the number of readers is less than S t − 2, where t < S 2 . In that same paper the authors pose a question of whether it is possible to relax the bound on readers, and at what cost, if semifast implementations are considered, i.e., implementations that have fast reads or fast writes.This paper provides an answer to this question. It is shown that one can obtain implementations where all writes are fast, i.e., involving a single round-trip communication, and where reads complete in one to two communication rounds under the assumption that no more than t < S 2 servers crash. Simulated scenarios included in this paper indicate that only a small fraction of reads require a second communication round. Interestingly the correctness of the implementation does not depend on the number of concurrent readers in the system. The solution is obtained with the help of non-unique virtual ids assigned to each reader, where the readers sharing a virtual id form a virtual node. For the proposed definition of semifast implementations it is shown that implementations satisfying certain assumptions are semifast if and only if the number of virtual ids in the system is less than S t − 2. This result is proved to be tight in terms of the required communication. It is shown that only a single complete two-round read operation may be necessary for each write operation. It is furthermore shown that no semifast implementation exists for the multi-reader, multi-writer model.

Abstract. This paper presents an efficient deterministic gossip algorithm for p synchronous, crash-prone, message-passing processors. The algorithm has time complexity T = O(log 2 p) and message complexity M = O(p 1+ε ), for any ε > 0. This substantially improves the message complexity of the previous best algorithm that has M = O(p 1.77 ), while maintaining the same time complexity. The strength of the new algorithm is demonstrated by constructing a deterministic algorithm for performing n tasks in this distributed setting. Previous solutions used coordinator or check-pointing approaches, immediately incurring a work penalty Ω(n + f · p) for f crashes, or relied on strong communication primitives, such as reliable broadcast, or had work too close to the trivial Θ(p · n) bound of oblivious algorithms. The new algorithm uses p crash-prone processors to perform n similar and idempotent tasks so long as one processor remains active. The work of the algorithm is W = O(n + p · min{f + 1, log 3 p}) and its message complexity is M = O(fp ε + p min{f + 1, log p}), for any ε > 0. This substantially improves the work complexity of previous solutions using simple point-to-point messaging, while "meeting or beating" the corresponding message complexity bounds. The new algorithms use communication graphs and permutations with certain combinatorial properties that are shown to exist. The algorithms are correct for any permutations, and in particular, the same expected bounds can be achieved using random permutations.

In this paper we explore the problem of achieving efficient packet transmission over unreliable links with worst case occurrence of errors. In such a setup, even an omniscient offline scheduling strategy cannot achieve stability of the packet queue, nor is it able to use up all the available bandwidth. Hence, an important first step is to identify an appropriate metric for measuring the efficiency of scheduling strategies in such a setting. To this end, we propose a relative throughput metric which corresponds to the long term competitive ratio of the algorithm with respect to the optimal. We then explore the impact of the error detection mechanism and feedback delay on our measure. We compare instantaneous error feedback with deferred error feedback, that requires a faulty packet to be fully received in order to detect the error. We propose algorithms for worst-case adversarial and stochastic packet arrival models, and formally analyze their performance. The relative throughput achieved by these algorithms is shown to be close to optimal by deriving lower bounds on the relative throughput of the algorithms and almost matching upper bounds for any algorithm in the considered settings. Our collection of results demonstrate the potential of using instantaneous feedback to improve the performance of communication systems in adverse environments.

Shareable data services providing consistency guarantees, such as atomicity (linearizability), make building distributed systems easier. However, combining linearizability with efficiency in practical algorithms is difficult. A reconfigurable linearizable data service, called RAMBO, was developed by Lynch and Shvartsman. This service guarantees consistency under dynamic conditions involving asynchrony, message loss, node crashes, and new node arrivals. The specification of the original algorithm is given at an abstract level aimed at concise presentation and formal reasoning about correctness. The algorithm propagates information by means of gossip messages. If the service is in use for a long time, the size and the number of gossip messages may grow without bound. This paper presents a consistent data service for long-lived objects that improves on RAMBO in two ways: it includes an incremental communication protocol and a leave service. The new protocol takes advantage of the local knowledge, and carefully manages the size of messages by removing redundant information, while the leave service allows the nodes to leave the system gracefully. The new algorithm is formally proved correct by forward simulation using levels of abstraction. An experimental implementation of the system was developed for networks-of-workstations. The paper also includes analytical and preliminary empirical results that illustrate the advantages of the new algorithm.

Abstract. This paper studies a trade-off between fault-tolerance and latency in implementations of atomic read/write objects in message-passing systems. In particular, considering fast or semifast quorum-based implementations, that is, implementations where all or respectively most read and write operations complete in a single communication round-trip, it is shown that such implementations are not robust due to the fact that they necessarily require a quorum system with a common intersection between its quorums. To trade speed for fault-tolerance, the notion of weak-semifast implementations is introduced. Here more than a single complete slow (two round-trip) read operation is allowed for each write operation (semifast implementations allow only one such slow read). A quorum-based algorithm is given next and it is formally shown that it constitutes a weak-semifast implementation of atomic registers. The algorithm uses the notion of Quorum Views to facilitate the characterization of all possible object timestamp distributions that a read operation may witness during its first communication round-trip. Noteworthy is that the algorithm allows fast read operations even if they are concurrent with other read and write operations. Finally, experimental results were gathered by simulating the algorithm using the NS-2 network simulator. The results show that under realistic conditions, less than 13% of read operations are slow, thus the overwhelming majority of operations take a single communication round-trip.

In this paper, we study the complexity of gossip in an asynchronous, message-passing fault-prone distributed system. In short, we show that an adaptive adversary can significantly hamper the spreading of a rumor, while an oblivious adversary cannot. This latter fact implies that there exist message-efficient asynchronous (randomized) consensus protocols, in the context of an oblivious adversary.In more detail, we summarize our results as follows. If the adversary is adaptive, we show that a randomized asynchronous gossip algorithm cannot terminate in fewer than O(f (d + δ)) time steps unless Ω(n + f 2 ) messages are exchanged, where n is the total number of processes, f is the number of tolerated crash failures, d is the maximum communication delay for the specific execution in question, and δ is the bound on relative process speeds in the specific execution. The lower bound result is to be contrasted with deterministic synchronous gossip algorithms that, even against an adaptive adversary, require only O( polylog(n)) time steps and O(n polylog(n)) messages.In the case of an oblivious adversary, we present three different randomized, asynchronous algorithms that provide different trade-offs between time complexity and message complexity. The first algorithm is based on the epidemic paradigm, and completes in O(using O(n log 3 n(d+δ)) messages, with high probability. The second algorithm relies on more rapid dissemination of the rumors, yielding a constant-time (w.r.t. n) gossip protocol: for every constant ε < 1, and for f ≤ n/2, there is a variant with time complexity O( 1 ε (d + δ)) and message complexity Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.