Distributed self-stabilizing algorithm for minimum spanning tree construction

Abstract. Minimal Spanning Tree (MST) problem in an arbitrary undirected graph is an important problem in graph theory and has extensive applications. Numerous algorithms are available to compute an MST. Our purpose here is to propose a self-stabilizing distributed algorithm for the MST problem and to prove its correctness. The algorithm utilizes an interesting result of [MP88]. We show the correctness of the proposed algorithm by using a new technique involving induction.

Mutual Exclusion Between Neighboring Nodes in a Tree That Stabilizes Using Read/Write Atomicity

. Our purpose in this paper is to propose a new protocol that can ensure mutual exclusion between neighboring nodes in a tree structured distributed system, i.e., under the given protocol no two neighboring nodes can execute their critical sections concurrently. This protocol can be used to run a serial model self stabilizing algorithm in a distributed environment that accepts as atomic operations only send a message, receive a message an update a state. Unlike the scheme in [1], our protocol does not use time-stamps (which are basically unbounded integers); our algorithm uses only bounded integers (actually, the integers can assume values only 0, 1, 2 and 3) and can be easily implemented. 1 Introduction Because of the popularity of the serial model and the relative ease of its use in designing new self-stabilizing algorithm, it is worthwhile to design lower level self-stabilizing protocols such that an algorithm developed for a serial model can be run in a distributed environment. Th..

A Self-Stabilizing Leader Election Algorithm for Tree Graphs

We propose a self stabilizing algorithm (protocol) for leader election in a tree graph. We show the correctness of the proposed algorithm by using a new technique involving induction. 1 Introduction In a distributed system the computing elements or nodes exchange information only by message passing. Every node has a set of local variables whose contents specify the local state of the node. The state of the entire system, called the global state, is the union of the local states of all the nodes in the system. Each node is allowed to have only a partial view of the global state, and this depends on the connectivity of the system and the propagation delay of different messages. Yet, the objective in a distributed system is to arrive at a desirable global final state (legitimate state), defined by some invariance relation on the global state. Systems that reach the legitimate state starting from any arbitrary (possibly illegitimate) state in a finite number of steps are called self-stabil..

Self-Stabilization: A New Paradigm for Fault Tolerance in Distributed Algorithm Design

Our purpose in the present paper is to present a brief overview of the relatively new paradigm of self-stabilization to provide fault tolerance in distributed systems. Stabilizing algorithms are optimistic in the sense that the distributed system may temporarily behave inconsistently but a return to correct system behavior is guranteed in finite time while traditional robust distributed algorithms follow a pessimistic approach in that it protects against the worst possible scenario which demands an assumption of the upper bound on the number of faults. 1 Introduction Robustness is one of the most important requirements of modern distributed systems. Different types of faults are likely to occur at various parts of the system. These systems go through the transient states because they are exposed to constant change of their environment. In a distributed system the computing elements or nodes exchange information only by message passing. One of the goals of a distributed system is that..

A self-stabilizing distributed algorithm to construct an arbitrary spanning tree of a connected graph

We propose a simple self-stabilizing distributed algorithm that maintains an arbitrary spanning tree in a connected graph. In proving the correctness of the algorithm we develop a new technique without using a bounded function (which is customary for proving correctness of self-stabilizing algorithms); the new approach is simple and can be potentially applied to proving correctness of other self-stabilizing algorithms.