Universal Loop-Free Super-Stabilization

We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree

A framework for proving the self-organization of dynamic systems

This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize different classes of self-organization through liveness and safety properties that both capture information re- garding the system entropy. We illustrate these classes through study cases. The first ones are two representative P2P overlays (CAN and Pas- try) and the others are specific implementations of \Omega (the leader oracle) and one-shot query abstractions for dynamic settings. Our study aims at understanding the limits and respective power of existing self-organized protocols and lays the basis of designing robust algorithm for dynamic systems

Compact Deterministic Self-Stabilizing Leader Election: The Exponential Advantage of Being Talkative

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 O(n\log^2 n) rounds. Our protocol has several attractive features that make it suitable for practical purposes. First, the communication model fits with the model used by existing compilers for real networks. Second, the size of the ring (or any upper bound on this size) needs not to be known by any node. Third, the node identifiers can be of various sizes. Finally, no synchrony assumption, besides a weakly fair scheduler, is assumed. Therefore, our result shows that, perhaps surprisingly, trading silence for exponential improvement in term of memory space does not come at a high cost regarding stabilization time or minimal assumptions

Stabilizing Inter-Domain Routing in the Internet

This paper reports the first self-stabilizing Border Gateway Protocol (BGP). BGP is the standard inter-domain routing protocol in the Internet. Self-stabilization is a technique to tolerate arbitrary transient faults. The routing instability in the Internet can occur due to errors in configuring the routing data structures, the routing policies, transient physical and data link problems, software bugs, and memory corruption. This instability can increase the network latency, slow down the convergence of the routing data structures, and can also cause the partitioning of networks. Most of the previous studies concentrated on routing policies to achieve the convergence of BGP while the oscillations due to transient faults were ignored. The purpose of self-stabilizing BGP is to solve the routing instability problem when this instability results from transient failures. The selfstabilizing BGP presented here provides a way to detect and automatically recover from this type of faults. Our protocol is combined with an existing protocol to make it resilient to policy conflicts as well

Asynchronous neighborhood task synchronization

Faults are likely to occur in distributed systems. The motivation for designing self-stabilizing system is to be able to automatically recover from a faulty state. As per Dijkstra\u27s definition, a system is self-stabilizing if it converges to a desired state from an arbitrary state in a finite number of steps. The paradigm of self-stabilization is considered to be the most unified approach to designing fault-tolerant systems. Any type of faults, e.g., transient, process crashes and restart, link failures and recoveries, and byzantine faults, can be handled by a self-stabilizing system; Many applications in distributed systems involve multiple phases. Solving these applications require some degree of synchronization of phases. In this thesis research, we introduce a new problem, called asynchronous neighborhood task synchronization ( NTS ). In this problem, processes execute infinite instances of tasks, where a task consists of a set of steps. There are several requirements for this problem. Simultaneous execution of steps by the neighbors is allowed only if the steps are different. Every neighborhood is synchronized in the sense that all neighboring processes execute the same instance of a task. Although the NTS problem is applicable in nonfaulty environments, it is more challenging to solve this problem considering various types of faults. In this research, we will present a self-stabilizing solution to the NTS problem. The proposed solution is space optimal, fault containing, fully localized, and fully distributed. One of the most desirable properties of our algorithm is that it works under any (including unfair) daemon. We will discuss various applications of the NTS problem

Compact routing in fault-tolerant distributed systems

A compact routing algorithm is a routing algorithm which reduces the space complexity of all-pairs shortest path routing. Compact routing protocols in distributed systems have been studied extensively as an attractive alternative to the traditional method of all-pairs shortest path routing. The use of compact routing protocols have several advantages. Compact routing schemes are not only more memory-efficient, but provide faster routing table lookup, more efficient broadcast scheme, and allow for a more scalable network. These routing schemes still maintain optimal or near-optimal routing paths. However, most of the compact routing protocols are not fault-tolerant. This thesis will first report the recent developments in the compact routing research. Several new methods for compact routing in fault-tolerant distributed systems will be presented and analyzed. The most important feature of the algorithms presented in this thesis is that they are self-stabilizing. The self-stabilization paradigm has been shown to be the most unified and all-inclusive approach to the design of fault-tolerant system. Additionally, these algorithms will address and solve several problems left unsolved by previous works. Relabelable and non-relabelable networks will be considered for both specific and arbitrary topologies

Self-stabilizing Border Gateway Protocol

The Border Gateway Protocol (BGP) is currently the only inter-domain routing protocol employed on the Internet. It is designed to exchange the reachability information among the autonomous systems in the global Internet. The Internet routing instability (or the rapid fluctuation of the network reachability information) is an important problem facing the Internet engineering community. With the wide availability of the Internet, the Internet failures may not only interrupt the daily routines of countless end-users, but also generate millions of dollars of loss in e-commerce. Since BGP has an impact on routing in the global Internet, the design and implementation of a robust and fault-tolerant Border Gateway Protocol is an important research topic; We achieve the fault-tolerance of BGP using the paradigm of self-stabilization. A self-stabilizing protocol, starting from an arbitrary state converges, within finite steps, to a state from where the system exhibits the desired behavior. In this thesis, we propose a self-stabilizing Border Gateway Protocol. Our design consists of mainly two phases: First, we investigate the Interior Gateway Protocols (IGP) which runs under the BGP. We design a self-stabilizing IGP. Because IGP provides the routing information inside an autonomous system, its stability is a crucial aspect of stabilization of the BGP. Then, we design a self-stabilizing BGP

Self-stabilizing k-clustering in mobile ad hoc networks

In this thesis, two silent self-stabilizing asynchronous distributed algorithms are given for constructing a k-clustering of a connected network of processes. These are the first self-stabilizing solutions to this problem. One algorithm, FLOOD, takes O( k) time and uses O(k log n) space per process, while the second algorithm, BFS-MIS-CLSTR, takes O(n) time and uses O(log n) space; where n is the size of the network. Processes have unique IDs, and there is no designated leader. BFS-MIS-CLSTR solves three problems; it elects a leader and constructs a BFS tree for the network, constructs a minimal independent set, and finally a k-clustering. Finding a minimal k-clustering is known to be NP -hard. If the network is a unit disk graph in a plane, BFS-MIS-CLSTR is within a factor of O(7.2552k) of choosing the minimal number of clusters; A lower bound is given, showing that any comparison-based algorithm for the k-clustering problem that takes o( diam) rounds has very bad worst case performance; Keywords: BFS tree construction, K-clustering, leader election, MIS construction, self-stabilization, unit disk graph

A self-stabilizing interval routing scheme in general networks

The Pivot Interval Routing (PIR) scheme [EGP98] divides the nodes in the network into pivots and clients of the pivots. A pivot acts as a center for the partition of the network formed by its clients. Each node can send messages directly only to a small subset of vertices in its nearby vicinity or to the pivots; An algorithm is called self-stabilizing [Dij74] if, starting from an arbitrary initial state, it is guaranteed to reach a correct state in finite time and with no exterior help. In this thesis, we present a self-stabilizing PIR algorithm. The algorithm starts with no knowledge of the network architecture and, eventually, each node builds its own routing table of size O(n1/2log3/2 n + Deltaupsilon, log n) bits with a total of O(n3/2 log3/2 n) bits. The stabilization time of the algorithm is O&parl0;dn1+logn &parr0; time units, where n is the number of nodes and d is the diameter of the network. (Abstract shortened by UMI.)