Self-stabilizing protocols must begin operating correctly even when started from an arbitrary state. The end-to-end problem is to ensure reliable message delivery across an unreliable network under the weakest possible guarantee from the network { that the sender and receiver are never separated by a cut of permanently failed links. In this paper we present the rst self-stabilizing end-to-end p...

Self-stabilizing protocols must begin operating correctly even when started from an arbitrary state. The end-to-end problem is to ensure reliable message delivery across an unreliable network under the weakest possible guarantee from the network { that the sender and receiver are never separated by a cut of permanently failed links. In this paper we present the rst self-stabilizing end-to-end p...

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of O(n log ∆) bits per n...

Self-stabilizing algorithms model distributed systems, which automatically recover from transient failures in the state of the system. The center of a graph comprises a set of vertices with minimum eccentricity. Farley and Proskurowski showed the linear time algorithm for locating the center of an outerplanar graph in the classical computing paradigm. The present paper investigates the selfstab...

A strongly heterogeneous strati ed elastic medium occupies a slab of nite thickness. The medium parameters vary randomly with correlation length of O( ). A pulse with O( ) wavelength enters the slab at one end. It travels coherently through the slab with a slowness near to that predicted by e ective medium theory. Relative to a certain realization-dependent co-moving frame of reference the puls...

The matching problem asks for a large set of disjoint edges in a graph. It is a problem that has received considerable attention in both the sequential and self-stabilizing literature. Previous work has resulted in self-stabilizing algorithms for computing a maximal ( 2 -approximation) matching in a general graph, as well as computing a 3 -approximation on more specific graph types. In the foll...

We propose two new self-stabilizing distributed algorithms for proper ∆+1 (∆ is the maximum degree of a node in the graph) colorings of arbitrary system graphs. Both algorithms are capable of working with multiple type of daemons (schedulers) as is the most recent algorithm by Gradinariu and Tixeuil [OPODIS’2000, 2000, pp. 55–70]. The first algorithm converges in O(m) moves while the second con...

During the past decades much of finite-dimensional systems theory has been generalized to infinite dimensions. However, there is one important flaw in this theory: it only guarantees complex solutions, even when the data is real. We show that the standard solutions of many classical problems with real data are also real. We call a (possibly matrixor operator-valued) holomorphic function G real ...