5 research outputs found
Separation of Circulating Tokens
Self-stabilizing distributed control is often modeled by token abstractions.
A system with a single token may implement mutual exclusion; a system with
multiple tokens may ensure that immediate neighbors do not simultaneously enjoy
a privilege. For a cyber-physical system, tokens may represent physical objects
whose movement is controlled. The problem studied in this paper is to ensure
that a synchronous system with m circulating tokens has at least d distance
between tokens. This problem is first considered in a ring where d is given
whilst m and the ring size n are unknown. The protocol solving this problem can
be uniform, with all processes running the same program, or it can be
non-uniform, with some processes acting only as token relays. The protocol for
this first problem is simple, and can be expressed with Petri net formalism. A
second problem is to maximize d when m is given, and n is unknown. For the
second problem, the paper presents a non-uniform protocol with a single
corrective process.Comment: 22 pages, 7 figures, epsf and pstricks in LaTe
A self-stabilizing 2/3-approximation algorithm for the maximum matching problem
International audienceThe 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 (-approximation) matching in a general graph, as well as computing a -approximation on more specific graph types. In the following we present the first self-stabilizing algorithm for finding a -approximation to the maximum matching problem in a general graph. We show that our new algorithm stabilizes in at most exponential time under a distributed adversarial daemon, and rounds under a distributed fair daemon, where is the number of nodes in the graph
A Self-Stabilizing Algorithm for Maximal Matching in Link-Register Model
International audienceThis paper presents a new distributed self-stabilizing algorithm solving the maximal matching problem under the fair distributed daemon. This is the first maximal matching algorithm in the link-register model under read/write atomicity. This work is composed of two parts. As we cannot establish a move complexity analysis under the fair distributed daemon, we first design an algorithm A_1 under the unfair distributed daemon dealing with some relaxed constraints on the communication model. Second, we adapt A_1 so that it can handle the fair distributed daemon, leading to the A_2 algorithm. We prove that algorithm A_1 stabilizes in O(m\Delta) moves and algorithm A_2 in O(m\Delta) rounds, with \Delta the maximum degree and m the number of edges