168 research outputs found
A self-stabilizing algorithm for detecting fundamental cycles in a graph with DFS spanning tree given
This paper presents a linear time self-stabilizing algorithm for detecting the set offundamental cycles on an undirected connected graph modelling asynchronous distributed system.The previous known algorithm has O(n^2) time complexity, whereas we prove that this one stabilizesafter O(n) moves. The distributed adversarial scheduler is considered. Both algorithms assume thatthe depth-search spanning tree of the graph is given. The output is given in a distributed manner asa state of variables in the nodes
Self-Stabilization in the Distributed Systems of Finite State Machines
The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems
Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction
Motivated by applications to sensor networks, as well as to many other areas,
this paper studies the construction of minimum-degree spanning trees. We
consider the classical node-register state model, with a weakly fair scheduler,
and we present a space-optimal \emph{silent} self-stabilizing construction of
minimum-degree spanning trees in this model. Computing a spanning tree with
minimum degree is NP-hard. Therefore, we actually focus on constructing a
spanning tree whose degree is within one from the optimal. Our algorithm uses
registers on bits, converges in a polynomial number of rounds, and
performs polynomial-time computation at each node. Specifically, the algorithm
constructs and stabilizes on a special class of spanning trees, with degree at
most . Indeed, we prove that, unless NP coNP, there are no
proof-labeling schemes involving polynomial-time computation at each node for
the whole family of spanning trees with degree at most . Up to our
knowledge, this is the first example of the design of a compact silent
self-stabilizing algorithm constructing, and stabilizing on a subset of optimal
solutions to a natural problem for which there are no time-efficient
proof-labeling schemes. On our way to design our algorithm, we establish a set
of independent results that may have interest on their own. In particular, we
describe a new space-optimal silent self-stabilizing spanning tree
construction, stabilizing on \emph{any} spanning tree, in rounds, and
using just \emph{one} additional bit compared to the size of the labels used to
certify trees. We also design a silent loop-free self-stabilizing algorithm for
transforming a tree into another tree. Last but not least, we provide a silent
self-stabilizing algorithm for computing and certifying the labels of a
NCA-labeling scheme
Exploration and Coverage with Swarms of Settling Agents
We consider several algorithms for exploring and filling an unknown,
connected region, by simple, airborne agents. The agents are assumed to be
identical, autonomous, anonymous and to have a finite amount of memory. The
region is modeled as a connected sub-set of a regular grid composed of square
cells. The algorithms described herein are suited for Micro Air Vehicles (MAV)
since these air vehicles enable unobstructed views of the ground below and can
move freely in space at various heights. The agents explore the region by
applying various action-rules based on locally acquired information Some of
them may settle in unoccupied cells as the exploration progresses. Settled
agents become virtual pheromones for the exploration and coverage process,
beacons that subsequently aid the remaining, and still exploring, mobile
agents. We introduce a backward propagating information diffusion process as a
way to implement a deterministic indicator of process termination and guide the
mobile agents. For the proposed algorithms, complete covering of the graph in
finite time is guaranteed when the size of the region is fixed. Bounds on the
coverage times are also derived. Extensive simulation results exhibit good
agreement with the theoretical predictions
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Working notes of the 1991 spring symposium on constraint-based reasoning
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