Two mobile agents starting at different nodes of an unknown network have to meet. This task is known in the literature as rendezvous. Each agent has a different label which is a positive integer known to it but unknown to the other agent. Agents move in an asynchronous way: the speed of agents may vary and is controlled by an adversary. The cost of a rendezvous algorithm is the total number of edge traversals by both agents until their meeting. The only previous deterministic algorithm solving this problem has cost exponential in the size of the graph and in the larger label. In this paper we present a deterministic rendezvous algorithm with cost polynomial in the size of the graph and in the length of the smaller label. Hence, we decrease the cost exponentially in the size of the graph and doubly exponentially in the labels of agents. As an application of our rendezvous algorithm we solve several fundamental problems involving teams of unknown size larger than 1 of labeled agents moving asynchronously in unknown networks. Among them are the following problems: \tt team size, in which every agent has to find the total number of agents; \tt leader election, in which all agents have to output the label of a single agent; \tt perfect renaming, in which all agents have to adopt new and different labels from the set $\{1,\dots,k\}$, where $k$ is the number of agents; and \tt gossiping, in which each agent has initially a piece of information (value) and all agents have to output all the values. Using our rendezvous algorithm, we solve all of these problems at cost polynomial in the size of the graph and in the smallest length of all labels of participating agents.

Two mobile agents starting at different nodes of an unknown network have to meet. This task is known in the literature as rendezvous. Each agent has a different label which is a positive integer known to it, but unknown to the other agent. Agents move in an asynchronous way: the speed of agents may vary and is controlled by an adversary. The cost of a rendezvous algorithm is the total number of edge traversals by both agents until their meeting. The only previous deterministic algorithm solving this problem has cost exponential in the size of the graph and in the larger label. In this paper we present a deterministic rendezvous algorithm with cost polynomial in the size of the graph and in the length of the smaller label. Hence we decrease the cost exponentially in the size of the graph and doubly exponentially in the labels of agents.

In this paper, we study the relationship between two fundammental problem in Robotics namely, leader election problem and pattern formation problem. In particular, we prove that both problems are equivalent for n≥4 in a fully asynchronous model, called CORDA, provided the robots share the same chirality.

A snap-stabilizing protocol, starting from any configuration, always behaves according to its specification. In this paper, we present a snap-stabilizing protocol to solve the message forwarding problem in a message-switched network. In this problem, we must manage resources of the system to deliver messages to any processor of the network. In this purpose, we use informations given by a routing algorithm. By the context of stabilization (in particular, the system starts in any configuration), these informations can be corrupted. So, the existence of a snap-stabilizing protocol for the message forwarding problem implies that we can ask the system to begin forwarding messages even if routing informations are initially corrupted. In this paper, we propose a snap-stabilizing algorithm (in the state model) for the following specification of the problem: Any message can be generated in a finite time. Any emitted message will be delivered to its destination once and only once in a finite time. This implies that our protocol can deliver any emitted message regardless of the state of routing tables in the initial configuration.

In this article, we show that some fundamental self- and snap-stabilizing wave protocols (e.g., token circulation, PIF , etc.) implicitly assume a very light property that we call BreakingIn . We prove that BreakingIn is strictly induced by self- and snap-stabilization. Combined with a transformer, BreakingIn allows to easily turn the non-fault-tolerant versions of those protocols into snap-stabilizing versions. Unlike the previous solutions, the transformed protocols are very efficient and work at least with the same daemon as the initial versions extended to satisfy BreakingIn . Finally, we show how to use an additional property of the transformer to design snap-stabilizing extensions of those fundamental protocols like Mutual Exclusion.

We present a self-stabilizing optimal (in terms of the distance) local routing algorithm (𝒮𝒪ℒℛ) for a wireless mobile ad hoc network. The distance may represent various metrics, including the real distance and the number of hops. The optimal routing for any node is computed for t closest nodes (called t -set) where t is an application-dependent parameter and is decided in advance. The locality is defined with respect to the t -set, not with respect to the direct neighbours. Our protocol is a particular case of distance vector routing protocol, where the number of entries in the routing table is limited to t . A self-stabilizing system has the ability to automatically recover to normal behaviour in case of transient faults without a centralized control. Each node can start in some arbitrary state and with no knowledge of the network architecture, but still eventually computes a correct routing table for the nodes in its t -set. If we assume that the t -set represents the set of destinations for which the shortest path needs to be computed, 𝒮𝒪ℒℛ becomes an optimal on-demand routing protocol. It can be extended to a global routing protocol by using features specific to other protocols (e.g. hierarchical routing, cluster routing, interval routing, etc.).

A snap-stabilizing protocol, starting from any arbitrary initial configuration, always behaves according to its specification. In this paper, we present the first snap-stabilizing depth-first search wave protocol for arbitrary rooted networks assuming an unfair daemon, i.e. assuming the weakest scheduling assumption (a preliminary version of this work was presented in OPODIS 2004, 8th International Conference on Principles of Distributed Systems, Grenoble (France)).

The group mutual exclusion (GME) problem was introduced by Joung. The GME solution allows n processes to share m mutually exclusive resources. We present several algorithms to solve the GME problem in token rings. The space requirement and the size of messages of all algorithms are bounded. So, the proposed algorithms solve the problem suggested by Joung, which is to obtain a solution using messages of bounded size. The time and space complexities of the first and second algorithms depend on n and m respectively. The first algorithm is more efficient when n ≪ m, whereas the second one when m ≪ n. The cost of the third algorithm is min(n, m). So, it is suitable for any type of network. However, the third solution is obtained with a message size of log(min(n, m)) extra bits. The third algorithm has an additional desirable property. It serves the requests in a first in first out manner. The fourth algorithm improves the bandwidth usage by avoiding the token circulation when no new requests are made for a different session. This property of the fourth algorithm can be incorporated into the other three algorithms.

We propose a general self-stabilizing scheme for solving any synchronization problem whose safety specification can be defined using a local property. We demonstrate the versatility of our scheme by showing that very memory-efficient solutions to many well-known problems (e.g., asynchronous phase clock, local mutual exclusion, local reader-writers, and local group mutual exclusion) can be derived using the proposed framework. We show that all these algorithms use a phase clock whose minimum size in terms of number of states per process is equal to CG + TG - 1, where CG is the length of the maximal cycle of the shortest maximum cycle basis if the graph contains cycles and 2 (otherwise) for tree networks, and TG is the length of the longest chordless cycle (i.e., hole) if the graph contains cycles and 2 for tree networks. In particular, for the asynchronous phase clock problem, our solution significantly improves all existing self-stabilizing solutions---all of them require quadratic space in terms of the number of states.As a by-product of our scheme, we present a silent bounded algorithm which can be used to transform any serial system into a distributed one. Thus, it answers an open question in [16], if there exists a bounded system transformation which is silent.

A snap-stabilizing protocol guarantees that the system always behaves according to its specification provided some processor initiated the protocol. We present how to snap-stabilize some important protocols, like Leader Election, Reset, Snapshot, and Termination Detection. We use a Snap-stabilizing Propagation of Information with Feedback protocol for arbitrary networks as the key module in the above transformation process. Finally, we design a universal transformer to provide a snap-stabilizing version of any protocol (which can be self-stabilized with the transformer of [15]).

Abstract In this paper, we present the first self‐stabilizing solution to the k‐out‐of‐ℓ exclusion problem on a ring. The k‐out‐of‐ℓ exclusion problem is a generalization of the well‐known mutual exclusion problem—there are ℓ units of the shared resources, any process can request k $(1 \leq k \leq \ell)$ units of the shared resources, and no resource unit can be allocated to more than one process at one time. The space requirement of the proposed algorithm is independent of ℓ for all processors except a special processor, called Root. The stabilization time is only 5n, where n is the size of the ring. Copyright © 2003 John Wiley & Sons, Ltd.

We present the first snap-stabilizing propagation of information with feedback (PIF) protocol in arbitrary networks. A snap-stabilizing protocol, starting from any arbitrary initial system configuration, always behaves according to its specification. Our protocol is distributed, deterministic, and does not use a pre-constructed spanning tree.

We propose a group mutual exclusion algorithm for unidirectional rings. Our algorithm does not require the processes to have any id. Moreover, processes maintain no special data structures to implement any queues. The space requirement of processes depends only on the number of shared resources, and is equal to 4/spl times/log(m+1)+2 bits. The size of messages is 2/spl times/log(m+1) bits only. Every resource request generates O(n/sup 2/) messages in the worst case, but zero messages in the best case.

We present a deterministic distributed Propagation of Information with Feedback (PIF) protocol in arbitrary rooted networks. The proposed algorithm does not use a preconstructed spanning tree. The protocol is self-stabilizing, meaning that starting from an arbitrary state (in response to an arbitrary perturbation modifying the memory state), it is guaranteed to behave according to its specification. Every PIF wave initiated by the root inherently creates a tree in the graph. So, the tree is dynamically created according to the progress of the PIF wave. This allows our PIF algorithm to take advantage of the relative speed of different components of the network. The proposed algorithm can be easily used to implement any self-stabilizing system which requires a (self-stabilizing) wave protocol running on an arbitrary network.

We present the first deterministic self-stabilizing network orientation algorithms. We present three protocols for arbitrary and asynchronous networks. All the protocols set up a chordal sense of direction in the network. The protocols are self-stabilizing, meaning that starting from an arbitrary state, the protocols are guaranteed to reach a state, in which all edge labels (assigned to the links) are valid (meaning, they satisfy the specification of the orientation problem).

In this paper, the phase clock algorithm which stabilizes on general graphs is studied on anonymous rings. The authors showed that this K-clock algorithm works with K/spl ges/2D, where D is the diameter of the graph. We prove that this algorithm works on unidirectional (bidirectional) rings iff K satisfies K>K'K/K'+n(2K>2K'-K/K'+n, respectively) where K' is the greatest divisor of K (K'/spl ne/K) and n is the size of the ring. From this characterization, we show that any ring stabilizes with some K<2D if K is odd. We also prove that, if K is prime, unidirectional and bidirectional rings stabilize with K<2[n/2]/spl sime/D and K<2[n/3]/spl sime/4D/3, respectively. Finally, we generalize the algorithm to synchronize any ring with any clock value.

Recently (1998), we introduced a new self-stabilizing PIF paradigm, called the Propagation of information with Feedback and Cleaning (PFC), for the rooted tree networks. In this paper, we propose the first self-stabilizing PIF scheme for the tree networks without sense of direction-the trees do not have a root and the processors do not maintain any ancestor. The proposed PIF scheme is based on the paradigm PFC. A PIF algorithm in trees without sense of direction is very useful in many applications because this allows to maintain only one spanning tree of the network instead of one per processor. The proposed algorithm requires 3 states per processor, and only 2 states for the initiator and leaves. This space requirement is optimal for both self-stabilizing and non-stabilizing PIF algorithms on tree networks. Thus, the processors need no extra space to stabilize the proposed PIF scheme.