5,355 research outputs found
Leader Election in Anonymous Rings: Franklin Goes Probabilistic
We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size
Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems
In many wireless networks, there is no fixed physical backbone nor
centralized network management. The nodes of such a network have to
self-organize in order to maintain a virtual backbone used to route messages.
Moreover, any node of the network can be a priori at the origin of a malicious
attack. Thus, in one hand the backbone must be fault-tolerant and in other hand
it can be useful to monitor all network communications to identify an attack as
soon as possible. We are interested in the minimum \emph{Connected Vertex
Cover} problem, a generalization of the classical minimum Vertex Cover problem,
which allows to obtain a connected backbone. Recently, Delbot et
al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant
approximation ratio of for this problem. In this paper, we propose a
distributed and self-stabilizing version of their algorithm with the same
approximation guarantee. To the best knowledge of the authors, it is the first
distributed and fault-tolerant algorithm for this problem. The approach
followed to solve the considered problem is based on the construction of a
connected minimal clique partition. Therefore, we also design the first
distributed self-stabilizing algorithm for this problem, which is of
independent interest
Improving Connectionist Energy Minimization
Symmetric networks designed for energy minimization such as Boltzman machines
and Hopfield nets are frequently investigated for use in optimization,
constraint satisfaction and approximation of NP-hard problems. Nevertheless,
finding a global solution (i.e., a global minimum for the energy function) is
not guaranteed and even a local solution may take an exponential number of
steps. We propose an improvement to the standard local activation function used
for such networks. The improved algorithm guarantees that a global minimum is
found in linear time for tree-like subnetworks. The algorithm, called activate,
is uniform and does not assume that the network is tree-like. It can identify
tree-like subnetworks even in cyclic topologies (arbitrary networks) and avoid
local minima along these trees. For acyclic networks, the algorithm is
guaranteed to converge to a global minimum from any initial state of the system
(self-stabilization) and remains correct under various types of schedulers. On
the negative side, we show that in the presence of cycles, no uniform algorithm
exists that guarantees optimality even under a sequential asynchronous
scheduler. An asynchronous scheduler can activate only one unit at a time while
a synchronous scheduler can activate any number of units in a single time step.
In addition, no uniform algorithm exists to optimize even acyclic networks when
the scheduler is synchronous. Finally, we show how the algorithm can be
improved using the cycle-cutset scheme. The general algorithm, called
activate-with-cutset, improves over activate and has some performance
guarantees that are related to the size of the network's cycle-cutset.Comment: See http://www.jair.org/ for any accompanying file
Exploration of Finite 2D Square Grid by a Metamorphic Robotic System
We consider exploration of finite 2D square grid by a metamorphic robotic
system consisting of anonymous oblivious modules. The number of possible shapes
of a metamorphic robotic system grows as the number of modules increases. The
shape of the system serves as its memory and shows its functionality. We
consider the effect of global compass on the minimum number of modules
necessary to explore a finite 2D square grid. We show that if the modules agree
on the directions (north, south, east, and west), three modules are necessary
and sufficient for exploration from an arbitrary initial configuration,
otherwise five modules are necessary and sufficient for restricted initial
configurations
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