In this paper we present the self-stabilizing implementation of a class of token based algorithms. In the current work we only consider interactions between weak nodes. They are uniform, they do not have unique identifiers, are static and their interactions are restricted to a subset of nodes called neighbours. While interacting, a pair of neighbouring nodes may create mobile agents (that materialize in the current work the token abstraction) that perform traversals of the network and accelerate the system stabilization. In this work we only explore the power of oblivious stateless agents.
Our work shows that the agent paradigm is an elegant distributed tool for achieving self-stabilization in Tiny Interaction Protocols (TIP). Nevertheless, in order to reach the full power of classical self-stabilizing algorithms more complex classes of agents have to be considered (e.g. agents with memory, identifiers or communication skills). Interestingly, our work proposes for the first time a model that unifies the recent studies in mobile robots(agents) that evolve in a discrete space and the already established population protocols paradigm.
We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing protocols. The first stage is a uniform randomized stabilizing {\em unique naming} protocol, and the second stage is a stabilizing {\em MDST} protocol, designed as a {\em fair composition} of Merlin--Segall's stabilizing protocol and a distributed deterministic stabilizing protocol solving the (MDST) problem. The resulting randomized distributed algorithm presented…
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 information given by a routing algorithm. By the context of stabilization (in particular, the system starts in an arbitrary configuration), this information can be corrupted. So, the existence of a snap-stabilizing protocol for the m…
In the population protocol model, many problems cannot be solved in a self-stabilizing way. However, global knowledge, such as the number of nodes in a network, sometimes allows us to design a self-stabilizing protocol for such problems. In this paper, we investigate the effect of global knowledge on the possibility of self-stabilizing population protocols in arbitrary graphs. Specifically, we clarify the solvability of the leader election problem, the ranking problem, the degree recognition problem, and the neighbor recognition problem by self-stabilizing population protocols with knowledge o…
We propose a self-stabilizing leader election protocol on directed rings in the model of population protocols. Given an upper bound $N$ on the population size $n$, the proposed protocol elects a unique leader within $O(nN)$ expected steps starting from any configuration and uses $O(N)$ states. This convergence time is optimal if a given upper bound $N$ is asymptotically tight, i.e., $N=O(n)$.
We fully characterize self-stabilizing functions in population protocols for complete interaction graphs. In particular, we investigate self-stabilization in systems of $n$ finite state agents in which a malicious scheduler selects an arbitrary sequence of pairwise interactions under a global fairness condition. We show a necessary and sufficient condition for self-stabilization. Specifically we show that functions without certain set-theoretic conditions are impossible to compute in a self-stabilizing manner. Our main contribution is in the converse, where we construct a self-stabilizing prot…
A self-stabilizing is naturally resilient to transients faults (that is, faults of finite duration). Recently, a new class of protocol appears. These protocols are self-stabilizing and are moreover resilient to a limited number of permanent faults. In this article, we interest in self-stabilizing protocols that tolerate very hard permanent faults: Byzantine faults. We introduce two new scheme of Byzantine containment in self-stabilizing systems. We show that, for the problem of BFS spanning tree construction, the well known self-stabilizing protocol min+1 provides without significant modificat…
In this paper we show that approximation can help reduce the space used for self-stabilization. In the classic \emph{state model}, where the nodes of a network communicate by reading the states of their neighbors, an important measure of efficiency is the space: the number of bits used at each node to encode the state. In this model, a classic requirement is that the algorithm has to be \emph{silent}, that is, after stabilization the states should not change anymore. We design a silent self-stabilizing algorithm for the problem of minimum spanning tree, that has a trade-off between the quality…
We consider the leader election problem in population protocol models. In pragmatic settings of population protocols, self-stabilization is a highly desired feature owing to its fault resilience and the benefit of initialization freedom. However, the design of self-stabilizing leader election is possible only under a strong assumption (i.e. the knowledge of the \emph{exact} size of a network) and rich computational resources (i.e. the number of states). Loose-stabilization, introduced by Sudo et al [Theoretical Computer Science, 2012], is a promising relaxed concept of self-stabilization to ad…
We consider the standard population protocol model, where (a priori) indistinguishable and anonymous agents interact in pairs according to uniformly random scheduling. The self-stabilizing leader election problem requires the protocol to converge on a single leader agent from any possible initial configuration. We initiate the study of time complexity of population protocols solving this problem in its original setting: with probability 1, in a complete communication graph. The only previously known protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time $Θ(n^…
In this paper, we present the first snap-stabilizing message forwarding protocol that uses a number of buffers per node being inde- pendent of any global parameter, that is 4 buffers per link. The protocol works on a linear chain of nodes, that is possibly an overlay on a large- scale and dynamic system, e.g., Peer-to-Peer systems, Grids. . . Provided that the topology remains a linear chain and that nodes join and leave "neatly", the protocol tolerates topology changes. We expect that this protocol will be the base to get similar results on more general topologies.
We extend the concept of monotonic searchability for self-stabilizing systems from one to multiple dimensions. A system is self-stabilizing if it can recover to a legitimate state from any initial illegal state. These kind of systems are most often used in distributed applications. Monotonic searchability provides guarantees when searching for nodes while the recovery process is going on. More precisely, if a search request started at some node $u$ succeeds in reaching its destination $v$, then all future search requests from $u$ to $v$ succeed as well. Although there already exists a self-sta…
The paper presents three self-stabilizing protocols for basic fair and reliable link communication primitives. We assume a link-register communication model under read/write atomicity, where every process can read from but cannot write into its neighbours' registers. The first primitive guarantees that any process writes a new value in its register(s) only after all its neighbours have read the previous value, whatever the initial scheduling of processes' actions. The second primitive implements a "weak rendezvous" communication mechanism by using an alternating bit protocol: whenever a proces…
We present a self-stabilizing protocol for an overlay network that constructs the Minimum Spanning Tree (MST) for an underlay that is modeled by a weighted tree. The weight of an overlay edge between two nodes is the weighted length of their shortest path in the tree. We rigorously prove that our protocol works correctly under asynchronous and non-FIFO message delivery. Further, the protocol stabilizes after $\mathcal{O}(N^2)$ asynchronous rounds where $N$ is the number of nodes in the overlay.
The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known ap- proaches in several ways. First, it makes fewer system hypotheses as the size of the netwo…
In this paper, we focus on the implementation of distributed programs in using a key-value store where the state of the nodes is stored in a replicated and partitioned data store to improve performance and reliability. Applications of such algorithms occur in weather monitoring, social media, etc. We argue that these applications should be designed to be stabilizing so that they recover from an arbitrary state to a legitimate state. Specifically, if we use a stabilizing algorithm then we can work with more efficient implementations that provide eventual consistency rather than sequential consi…
A self-stabilizing protocol tolerates by definition transient faults (faults of finite duration). Recently, a new class of self-stabilizing protocols that are able to tolerate a given number of permanent faults. In this paper, we focus on self-stabilizing protocols able to tolerate Byzantine faults, that is faults that introduce an arbitrary behaviour. We focus on strict-stabilization in which the system have to contain the effects of Byzantine faults. Specificaly, we study the possibility to construct in a self-stabilizing way a maximal matching in a network where an arbitrary number of proce…
A self-stabilizing protocol provides by definition a tolerance to transient failures. Recently, a new class of self-stabilizing protocols appears. These protocols provides also a tolerance to a given number of permanent failures. In this article, we are interested in self-stabilizing protocols that deal with Byzantines failures. We prove that, for some problems which not allow strict stabilization (see [Nesterenko,Arora,2002]), there exist solutions that tolerates Byzantine faults if we define a new criteria of tolerance.
This paper considers the basic $\mathcal{PULL}$ model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of $n$ agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let …
We consider congestion control in peer-to-peer distributed systems. The problem can be reduced to the following scenario: Consider a set $V$ of $n$ peers (called clients in this paper) that want to send messages to a fixed common peer (called server in this paper). We assume that each client $v \in V$ sends a message with probability $p(v) \in [0,1)$ and the server has a capacity of $σ\in \mathbb{N}$, i.e., it can recieve at most $σ$ messages per round and excess messages are dropped. The server can modify these probabilities when clients send messages. Ideally, we wish to converge to a state …
A self-stabilizing protocol has the capacity to recover a legitimate behavior whatever is its initial state. The majority of works in self-stabilization assume a shared memory model or a communication using reliable and FIFO channels. In this article, we interest in self-stabilizing systems using bounded but non reliable and non FIFO channels. We propose a stabilizing communication protocol with optimal fault resilience. In more details, this protocol simulates a reliable and FIFO channel and ensures a minimal number of looses, duplications, creations, and re-ordering of messages.
This paper focuses on compact deterministic self-stabilizing solutions for the leader election problem. When the protocol is required to be \emph{silent} (i.e., when communication content remains fixed from some point in time during any execution), there exists a lower bound of Omega(\log n) bits of memory per node participating to the leader election (where n denotes the number of nodes in the system). This lower bound holds even in rings. We present a new deterministic (non-silent) self-stabilizing protocol for n-node rings that uses only O(\log\log n) memory bits per node, and stabilizes in…
We present a loosely-stabilizing phase clock for population protocols. In the population model we are given a system of $n$ identical agents which interact in a sequence of randomly chosen pairs. Our phase clock is leaderless and it requires $O(\log n)$ states. It runs forever and is, at any point of time, in a synchronous state w.h.p. When started in an arbitrary configuration, it recovers rapidly and enters a synchronous configuration within $O(n\log n)$ interactions w.h.p. Once the clock is synchronized, it stays in a synchronous configuration for at least poly $n$ parallel time w.h.p. We u…
We propose a protocol (called RBO) for broadcasting long streams of single-packet messages over radio channel for tiny, battery powered, receivers. The messages are labeled by the keys from some linearly ordered set. The sender repeatedly broadcasts a sequence of many (possibly millions) of messages, while each receiver is interested in reception of a message with a specified key within this sequence. The transmission is arranged so that the receiver can wake up in arbitrary moment and find the nearest transmission of its searched message. Even if it does not know the position of the message i…
Searching for other participants is one of the most important operations in a distributed system. We are interested in topologies in which it is possible to route a packet in a fixed number of hops until it arrives at its destination. Given a constant $d$, this paper introduces a new self-stabilizing protocol for the $q$-ary $d$-dimensional de Bruijn graph ($q = \sqrt[d]{n}$) that is able to route any search request in at most $d$ hops w.h.p., while significantly lowering the node degree compared to the clique: We require nodes to have a degree of $\mathcal O(\sqrt[d]{n})$, which is asymptotic…
While a lot of research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures. Considering crashing peers in peer-to-peer networks, it should not be taken for granted that a distributed data structure remains intact. In this work, we present a self-stabilizing protocol for a distributed data structure called the hashed Patricia Trie (Kniesburges and Scheideler WALCOM'11) that enables efficient prefix search on a set of keys. The data structure has a wide area of applications inc…
Distributed applications are commonly based on overlay networks interconnecting their sites so that they can exchange information. For these overlay networks to preserve their functionality, they should be able to recover from various problems like membership changes or faults. Various self-stabilizing overlay networks have already been proposed in recent years, which have the advantage of being able to recover from any illegal state, but none of these networks can give any guarantees on its functionality while the recovery process is going on. We initiate research on overlay networks that are…
For overlay networks, the ability to recover from a variety of problems like membership changes or faults is a key element to preserve their functionality. In recent years, various self-stabilizing overlay networks have been proposed that have the advantage of being able to recover from any illegal state. However, the vast majority of these networks cannot give any guarantees on its functionality while the recovery process is going on. We are especially interested in searchability, i.e., the functionality that search messages for a specific identifier are answered successfully if a node with t…
Byzantine agreement algorithms typically assume implicit initial state consistency and synchronization among the correct nodes and then operate in coordinated rounds of information exchange to reach agreement based on the input values. The implicit initial assumptions enable correct nodes to infer about the progression of the algorithm at other nodes from their local state. This paper considers a more severe fault model than permanent Byzantine failures, one in which the system can in addition be subject to severe transient failures that can temporarily throw the system out of its assumption b…
From data centers to IoT devices to Internet-based applications, overlay networks have become an important part of modern computing. Many of these overlay networks operate in fragile environments where processes are susceptible to faults which may perturb a node's state and the network topology. Self-stabilizing overlay networks have been proposed as one way to manage these faults, promising to build or restore a particular topology from any initial configuration or after the occurrence of any transient fault. To date there have been several self-stabilizing protocols designed for overlay netw…
The population protocol model describes a network of anonymous agents that interact asynchronously in pairs chosen at random. Each agent starts in the same initial state $s$. We introduce the *dynamic size counting* problem: approximately counting the number of agents in the presence of an adversary who at any time can remove any number of agents or add any number of new agents in state $s$. A valid solution requires that after each addition/removal event, resulting in population size $n$, with high probability each agent "quickly" computes the same constant-factor estimate of the value $\log_…
$P_c\varepsilonκ_{max}$-Means++: Adapt-$P$ Driven by Energy and Distance Quality Probabilities Based on $κ$-Means++ for the Stable Election Protocol (SEP)
This paper proposes the first implementation of a self-stabilizing regular register emulated by $n$ servers that is tolerant to both mobile Byzantine agents, and \emph{transient failures} in a round-free synchronous model. Differently from existing Mobile Byzantine tolerant register implementations, this paper considers a more powerful adversary where (i) the message delay (i.e., $δ$) and the period of mobile Byzantine agents movement (i.e., $Δ$) are completely decoupled and (ii) servers are not aware of their state i.e., they do not know if they have been corrupted or not by a mobile Byzantin…
Self-stabilizing protocols enable distributed systems to recover correct behavior starting from any arbitrary configuration. In particular, when processors communicate by message passing, fake messages may be placed in communication links by an adversary. When the number of such fake messages is unknown, self-stabilization may require huge resources: (a) generic solutions (a.k.a. data link protocols) require unbounded resources, which makes them unrealistic to deploy and (b) specific solutions (e.g., census or tree construction) require $O(n\log n)$ or $O(Δ\log n)$ bits of memory per node, whe…
We consider the problem of managing a dynamic heterogeneous storage system in a distributed way so that the amount of data assigned to a host in that system is related to its capacity. Two central problems have to be solved for this: (1) organizing the hosts in an overlay network with low degree and diameter so that one can efficiently check the correct distribution of the data and route between any two hosts, and (2) distributing the data among the hosts so that the distribution respects the capacities of the hosts and can easily be adapted as the set of hosts or their capacities change. We p…
We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $Σ$. The system must converge toward a consensus state in which all, or almost all nodes, hold the same opinion. Moreover, this opinion should be \emph{valid}, i.e., it should be one among those initially present in the system. This condition should be met even in the presence of an adaptive, malicious adversary who can modify the opinions of a bounded number of nodes in every round. We consider the \…
Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players' preferences. Recognizing an equilibrium in this setting is a distributed computational task. Self-stabilizing uncoupled dynamics, then, have both resilience to arbitrary initial states and distribution of knowledge. We study these dynamics by analyzing their behavior in a bounded-recall synchronous environment. We determine, for every "size" of game, the minimu…
The majority of the literature on consensus assumes that protocols are jointly started at all nodes of the distributed system. We show how to remove this problematic assumption in semi-synchronous systems, where messages delays and relative drifts of local clocks may vary arbitrarily within known bounds. Our framework is self-stabilizing and efficient both in terms of communication and time; more concretely, compared to a synchronous start in a synchronous model of a non-self-stabilizing protocol, we achieve a constant-factor increase in the time and communicated bits to complete an instance, …
In dynamic wireless ad-hoc networks (DynWANs), autonomous computing devices set up a network for the communication needs of the moment. These networks require the implementation of a medium access control (MAC) layer. We consider MAC protocols for DynWANs that need to be autonomous and robust as well as have high bandwidth utilization, high predictability degree of bandwidth allocation, and low communication delay in the presence of frequent topological changes to the communication network. Recent studies have shown that existing implementations cannot guarantee the necessary satisfaction of t…
For reaching fast and efficient self-stabilizing Byzantine pulse synchronization (SSBPS) upon the bounded-delay message-passing networks, we consider the peaceable SSBPS problem where the resource occupation in the stabilized system is required to be as sparse as possible and the stabilization of the system is required to be as fast as possible. To solve it, the decoupled absorption process and emergency process are investigated under a general framework. The constant-time two-stage absorption process and more than one kind of emergency process are provided in integrating the merits of tempora…
Self-stabilization ensures that, after any transient fault, the system recovers in a finite time and eventually exhibits. Speculation consists in guaranteeing that the system satisfies its requirements for any execution but exhibits significantly better performances for a subset of executions that are more probable. A speculative protocol is in this sense supposed to be both robust and efficient in practice. We introduce the notion of speculative stabilization which we illustrate through the mutual exclusion problem. We then present a novel speculatively stabilizing mutual exclusion protocol. …
Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. Combining these two properties proved difficult: it is impossible to contain the spatial impact of Byzantine nodes in a self-stabilizing context for global tasks such as tree orientation and tree construction. We present and illustrate a new concept of Byzantine contai…
