A New Self-Stabilizing Maximal Matching Algorithm

The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon, the sequential adversarial daemon, as well as the synchronous daemon. In the following we present a single self-stabilizing algorithm for this problem that unites all of these algorithms in that it stabilizes in the same number of moves as the previous best algorithms for the sequential adversarial, the distributed fair, and the synchronous daemon. In addition, the algorithm improves the previous best moves complexities for the distributed adversarial daemon from O(n^2) and O(delta m) to O(m) where n is the number of processes, m is thenumber of edges, and delta is the maximum degree in the graph

A self-stabilizing algorithm for 3-edgeconnectivity

Abstract: Self-stabilization is a theoretical framework for fault-tolerance without external assistance. Adoption of self-stabilization in distributed systems has received considerable research interest over the last decade. In this paper, we propose a self-stabilizing algorithm for 3-edgeconnectivity of an asynchronous distributed model of computation. A self-stabilizing depth-first search algorithm is run concurrently to build a depth-first search spanning tree of the system. Once such a tree is constructed, all the 3-edge-connected components of the system can be detected in O(h) rounds, where h is the height of the depth-first search tree. The result of computation is kept in a distributed fashion in the sense that, upon stabilization of the algorithm, each processor knows all other processors that are 3-edge-connected to it. The space complexity of our algorithm is O(n log ∆) bits per processor, where ∆ is an upper bound on the degree of a processor. This space complexity is same as that of the self-stabilizing depth-first search algorithm

Self-stabilizing algorithms for finding centers and medians of trees

Locating a center or a median in a graph is a fundamental graph-theoretic problem. Centers and medians are especially important in distributed systems because they are ideal locations for placing resources that need to be shared among different processes in a network. This paper presents simple self-stabilizing algorithms for locating centers and medians of trees. Since these algorithms are self-stabilizing, they can tolerate transient failures. In addition, they can automatically adjust to a dynamically changing tree topology. After the algorithms are presented, their correctness is proven and upper bounds on their time complexity are established. Finally, extensions of our algorithms to trees with arbitrary, positive edge costs are sketched

Self-stabilizing Algorithm for Maximal Graph Partitioning into Triangles

International audienceThe graph partitioning problem consists of dividing a graph into parts or partitions which satisfy some specifications. This problem has several applications such image segmentation, load balancing and communities’ detection. Unfortunately, graph partitioningis known to be NP-complete. In this paper, we present, the first self-stabilizing algorithm for maximal partitioning arbitrary graph into triangles (SPT), then we present the correctness and convergence proofs of the proposed algorithm

Distributed Weighted Matching

In this paper, we present fast and fully distributed algorithms for matching in weighted trees and general weighted graphs. The time complexity as well as the approximation ratio of the tree algorithm is constant. In particular, the approximation ratio is 4. For the general graph algorithm we prove a constant ratio bound of 5 and a polylogarithmic time complexity of O(log n)

An Efficient Silent Self-stabilizing 1-Maximal Matching Algorithm Under Distributed Daemon Without Global Identifiers

International audienceWe propose a new self-stabilizing 1-maximal matching algorithm that works under the distributed unfair daemon for arbitrarily shaped networks without cycle whose length is a multiple of three. The 1-maximal matching is a 2/3-approximation of a maximum matching, a significant improvement over the 1/2-approximation that is guaranteed by a maximal matching. Our algorithm is as efficient (its stabilization time is O(e) moves, where e denotes the number of edges in the network) as the best known algorithm operating under the weaker central daemon. It significantly outperforms the only known algorithm for the distributed daemon (with O(e) moves vs. O(2^n*δn) moves, where δ denotes the maximum degree of the network, and n its number of nodes), while retaining its silence property (after stabilization, its output remains fixed)

Randomized Self-stabilizing Algorithms for Wireless Sensor Networks

Wireless sensor networks (WSNs) pose challenges not present in classical distributed systems: resource limitations, high failure rates, and ad hoc deployment. The lossy nature of wireless communication can lead to situations, where nodes lose synchrony and programs reach arbitrary states. Traditional approaches to fault tolerance like replication or global resets are not feasible. In this work, the concept of self-stabilization is applied to WSNs. The majority of self-stabilizing algorithms found in the literature is based on models not suitable for WSNs: shared memory model, central daemon scheduler, unique processor identifiers, and atomicity. This paper proposes problem-independent transformations for algorithms that stabilize under the central daemon scheduler such that they meet the demands of a WSN. The transformed algorithms use randomization and are probabilistically self-stabilizing. This work allows to utilize many known self-stabilizing algorithms in WSNs. The proposed transformations are evaluated using simulations and a real WSN