Self-stabilizing tree algorithms

Designers of distributed algorithms have to contend with the problem of making the algorithms tolerant to several forms of coordination loss, primarily faulty initialization. The processes in a distributed system do not share a global memory and can only get a partial view of the global state. Transient failures in one part of the system may go unnoticed in other parts and thus cause the system to go into an illegal state. If the system were self-stabilizing, however, it is guaranteed that it will return to a legal state after a finite number of state transitions. This thesis presents and proves self-stabilizing algorithms for calculating tree metrics and for achieving mutual exclusion on a tree structured distributed system

Dining philosophers with masking tolerance to crash faults

We examine the tolerance of dining philosopher algorithms subject to process crash faults in arbitrary conflict graphs. This classic problem is unsolvable in asynchronous message-passing systems subject to even a single crash fault. By contrast, dining can be solved in synchronous systems capable of implementing the perfect failure detector P (from the Chandra-Toueg hierarchy). We show that dining is also solvable in weaker timing models using a combination of the trusting detector T and the strong detector S; Our approach extends and composes two currents of previous research. First, we define a parametric generalization of Lynch’s classic algorithm for hierarchical resource allocation. Our construction converts any mutual exclusion algorithm into a valid dining algorithm. Second, we consider the fault-tolerant mutual exclusion algorithm (FTME) of Delporte-Gallet, et al., which uses T and the strong detector S to mask crash faults in any environment. We instantiate our dining construction with FTME, and prove that the resulting dining algorithm guarantees masking tolerance to crash faults. Our contribution (1) defines a new construction for transforming mutual exclusion algorithms into dining algorithms, and (2) demonstrates a better upper-bound on the fault-detection capabilities necessary to mask crash faults in dining philosophers

Permission-based fault tolerant mutual exclusion algorithm for mobile Ad Hoc networks

This study focuses on resolving the problem of mutual exclusion in mobile ad hoc networks. A Mobile Ad Hoc Network (MANET) is a wireless network without fixed infrastructure. Nodes are mobile and topology of MANET changes very frequently and unpredictably. Due to these limitations, conventional mutual exclusion algorithms presented for distributed systems (DS) are not applicable for MANETs unless they attach to a mechanism for dynamic changes in their topology. Algorithms for mutual exclusion in DS are categorized into two main classes including token-based and permission-based algorithms. Token-based algorithms depend on circulation of a specific message known as token. The owner of the token has priority for entering the critical section. Token may lose during communications, because of link failure or failure of token host. However, the processes for token-loss detection and token regeneration are very complicated and time-consuming. Token-based algorithms are generally non-fault-tolerant (although some mechanisms are utilized to increase their level of fault-tolerance) because of common problem of single token as a single point of failure. On the contrary, permission-based algorithms utilize the permission of multiple nodes to guarantee mutual exclusion. It yields to high traffic when number of nodes is high. Moreover, the number of message transmissions and energy consumption increase in MANET by increasing the number of mobile nodes accompanied in every decision making cycle. The purpose of this study is to introduce a method of managing the critical section,named as Ancestral, having higher fault-tolerance than token-based and fewer message transmissions and traffic rather that permission-based algorithms. This method makes a tradeoff between token-based and permission-based. It does not utilize any token, that is similar to permission-based, and the latest node having the critical section influences the entrance of the next node to the critical section, that is similar to token-based algorithms. The algorithm based on ancestral is named as DAD algorithms and increases the availability of fully connected network between 2.86 to 59.83% and decreases the number of message transmissions from 4j-2 to 3j messages (j as number of nodes in partition). This method is then utilized as the basis of dynamic ancestral mutual exclusion algorithm for MANET which is named as MDA. This algorithm is presented and evaluated for different scenarios of mobility of nodes, failure, load and number of nodes. The results of study show that MDA algorithm guarantees mutual exclusion,dead lock freedom and starvation freedom. It improves the availability of CS to minimum 154.94% and 113.36% for low load and high load of CS requests respectively compared to other permission-based lgorithm.Furthermore, it improves response time up to 90.69% for high load and 75.21% for low load of CS requests. It degrades the number of messages from n to 2 messages in the best case and from 3n/2 to n in the worst case. MDA algorithm is resilient to transient partitioning of network that is normally occurs due to failure of nodes or links

Resource efficient redundancy using quorum-based cycle routing in optical networks

In this paper we propose a cycle redundancy technique that provides optical networks almost fault-tolerant point-to-point and multipoint-to-multipoint communications. The technique more importantly is shown to approximately halve the necessary light-trail resources in the network while maintaining the fault-tolerance and dependability expected from cycle-based routing. For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Optimal communication quorum sets forming optical cycles based on light-trails have been shown to flexibly and efficiently route both point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle routing techniques will use pairs of cycles to achieve both routing and fault-tolerance, which uses substantial resources and creates the potential for underutilization. Instead, we intentionally utilize redundancy within the quorum cycles for fault-tolerance such that almost every point-to-point communication occurs in more than one cycle. The result is a set of cycles with 96.60% - 99.37% fault coverage, while using 42.9% - 47.18% fewer resources.Comment: 17th International Conference on Transparent Optical Networks (ICTON), 5-9 July 2015. arXiv admin note: substantial text overlap with arXiv:1608.05172, arXiv:1608.0516

Automated Synthesis of Distributed Self-Stabilizing Protocols

In this paper, we introduce an SMT-based method that automatically synthesizes a distributed self-stabilizing protocol from a given high-level specification and network topology. Unlike existing approaches, where synthesis algorithms require the explicit description of the set of legitimate states, our technique only needs the temporal behavior of the protocol. We extend our approach to synthesize ideal-stabilizing protocols, where every state is legitimate. We also extend our technique to synthesize monotonic-stabilizing protocols, where during recovery, each process can execute an most once one action. Our proposed methods are fully implemented and we report successful synthesis of well-known protocols such as Dijkstra's token ring, a self-stabilizing version of Raymond's mutual exclusion algorithm, ideal-stabilizing leader election and local mutual exclusion, as well as monotonic-stabilizing maximal independent set and distributed Grundy coloring

Synchronous Counting and Computational Algorithm Design

Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates $f$ Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states. This work consists of two parts. In the first part, we use computational techniques (often known as synthesis) to construct very compact deterministic algorithms for the first non-trivial case of $f = 1$. While no algorithm exists for $n < 4$, we show that as few as 3 states per node are sufficient for all values $n \ge 4$. Moreover, the problem cannot be solved with only 2 states per node for $n = 4$, but there is a 2-state solution for all values $n \ge 6$. In the second part, we develop and compare two different approaches for synthesising synchronous counting algorithms. Both approaches are based on casting the synthesis problem as a propositional satisfiability (SAT) problem and employing modern SAT-solvers. The difference lies in how to solve the SAT problem: either in a direct fashion, or incrementally within a counter-example guided abstraction refinement loop. Empirical results suggest that the former technique is more efficient if we want to synthesise time-optimal algorithms, while the latter technique discovers non-optimal algorithms more quickly.Comment: 35 pages, extended and revised versio