Search

Given a boolean predicate Π on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for Π is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying Π. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size n of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of O(log log n) bits per node in any n-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use (log log n)-bit per node registers in some n-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms. [ABSTRACT FROM AUTHOR]

Abstract A pair of agents (robots) are moving in a graph with the goal of meeting at the same node or while traversing the same edge. An asynchronous adversary knows the prescribed walks of the two agents and is in complete control of the speed of each agent during its walk. We provide a complete characterization of pairs of walks that enforce rendezvous against an asynchronous adversary after traversing a given number of edges. The characterization is efficient in that it can be checked in polynomial time. We argue that the certificate of rendezvous enforcement that is produced by the checking algorithm contains a wealth of information on why rendezvous is enforced. [ABSTRACT FROM AUTHOR]

Routing protocols are at the core of distributed systems performances, especially in the presence of faults. A classical approach to this problem is to build a spanning tree of the distributed system. Numerous spanning tree construction algorithms depending on the optimized metric exist (total weight, height, distance with respect to a particular process, …) both in fault-free and faulty environments. In this paper, we aim at optimizing the diameter of the spanning tree by constructing a minimum diameter spanning tree. We target environments subject to transient faults ( i.e. faults of finite duration). Hence, we present a self-stabilizing algorithm for the minimum diameter spanning tree construction problem in the state model. Our protocol has the following attractive features. It is the first algorithm for this problem that operates under the unfair and distributed adversary (or daemon ). In other words, no restriction is made on the asynchronous behavior of the system. Second, our algorithm needs only O ( log n ) bits of memory per process (where n is the number of processes), that improves the previous result by a factor n . These features are not achieved to the detriment of the convergence time, which stays polynomial. [ABSTRACT FROM AUTHOR]