Termination Detection of Local Computations

Contrary to the sequential world, the processes involved in a distributed system do not necessarily know when a computation is globally finished. This paper investigates the problem of the detection of the termination of local computations. We define four types of termination detection: no detection, detection of the local termination, detection by a distributed observer, detection of the global termination. We give a complete characterisation (except in the local termination detection case where a partial one is given) for each of this termination detection and show that they define a strict hierarchy. These results emphasise the difference between computability of a distributed task and termination detection. Furthermore, these characterisations encompass all standard criteria that are usually formulated : topological restriction (tree, rings, or triangu- lated networks ...), topological knowledge (size, diameter ...), and local knowledge to distinguish nodes (identities, sense of direction). These results are now presented as corollaries of generalising theorems. As a very special and important case, the techniques are also applied to the election problem. Though given in the model of local computations, these results can give qualitative insight for similar results in other standard models. The necessary conditions involve graphs covering and quasi-covering; the sufficient conditions (constructive local computations) are based upon an enumeration algorithm of Mazurkiewicz and a stable properties detection algorithm of Szymanski, Shi and Prywes

A System for Distributed Mechanisms: Design, Implementation and Applications

We describe here a structured system for distributed mechanism design appropriate for both Intranet and Internet applications. In our approach the players dynamically form a network in which they know neither their neighbours nor the size of the network and interact to jointly take decisions. The only assumption concerning the underlying communication layer is that for each pair of processes there is a path of neighbours connecting them. This allows us to deal with arbitrary network topologies. We also discuss the implementation of this system which consists of a sequence of layers. The lower layers deal with the operations that implement the basic primitives of distributed computing, namely low level communication and distributed termination, while the upper layers use these primitives to implement high level communication among players, including broadcasting and multicasting, and distributed decision making. This yields a highly flexible distributed system whose specific applications are realized as instances of its top layer. This design is implemented in Java. The system supports at various levels fault-tolerance and includes a provision for distributed policing the purpose of which is to exclude `dishonest' players. Also, it can be used for repeated creation of dynamically formed networks of players interested in a joint decision making implemented by means of a tax-based mechanism. We illustrate its flexibility by discussing a number of implemented examples.Comment: 36 pages; revised and expanded versio

Distributed anonymous function computation in information fusion and multiagent systems

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we exhibit a class of non-computable functions, and prove that every function outside this class can at least be approximated. The problem of computing averages in a distributed manner plays a central role in our development

Distributed anonymous discrete function computation

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes. In this model, each node has bounded computation and storage capabilities that do not grow with the network size. Furthermore, each node only knows its neighbors, not the entire graph. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we provide a necessary condition for computability which we show to be nearly sufficient, in the sense that every function that satisfies this condition can at least be approximated. The problem of computing suitably rounded averages in a distributed manner plays a central role in our development; we provide an algorithm that solves it in time that grows quadratically with the size of the network

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations

Enabling Correct Interest Forwarding and Retransmissions in a Content Centric Network

We show that the mechanisms used in the name data networking (NDN) and the original content centric networking (CCN) architectures may not detect Interest loops, even if the network in which they operate is static and no faults occur. Furthermore, we show that no correct Interest forwarding strategy can be defined that allows Interest aggregation and attempts to detect Interest looping by identifying Interests uniquely. We introduce SIFAH (Strategy for Interest Forwarding and Aggregation with Hop-Counts), the first Interest forwarding strategy shown to be correct under any operational conditions of a content centric network. SIFAH operates by having forwarding information bases (FIBs) store the next hops and number of hops to named content, and by having each Interest state the name of the requested content and the hop count from the router forwarding an Interest to the content. We present the results of simulation experiments using the ndnSIM simulator comparing CCN and NDN with SIFAH. The results of these experiments illustrate the negative impact of undetected Interest looping when Interests are aggregated in CCN and NDN, and the performance advantages of using SIFAH

Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots

We consider a team of $k$ identical, oblivious, asynchronous mobile robots that are able to sense (\emph{i.e.}, view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by \emph{deterministic} robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the \emph{exploration} problem of anonymous unoriented rings of any size. It is known that $\Theta(\log n)$ robots are necessary and sufficient to solve the problem with $k$ deterministic robots, provided that $k$ and $n$ are coprime. By contrast, we show that \emph{four} identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive