10,910 research outputs found
Competitive Self-Stabilizing k-Clustering
A k-cluster of a graph is a connected non-empty subgraph C of radius at most k, i.e., all members of C are within distance k of a particular node of C, called the clusterhead of C. A k-clustering of a graph is a partitioning of the graph into distinct k-clusters. Finding a mini-mum cardinality k-clustering is known to be NP-hard. In this paper, we propose a silent self-stabilizing asynchronous distributed algorithm for con-structing a k-clustering of any connected network with unique IDs. Our algorithm stabilizes in O(n) rounds, using O(log n) space per process, where n is the number of processes. In the general case, our algorithm constructs O(nk) k-clusters. If the network is a Unit Disk Graph (UDG), then our algorithm is 7.2552k + O(1)-competitive, that is, the number of k-clusters constructed by the algorithm is at most 7.2552k + O(1) times the minimum possible number of k-clusters in any k-clustering of the same network. More generally, if the net-work is an Approximate Disk Graph (ADG) with approximation ratio λ, then our algorithm is 7.2552λ2k +O(λ)-competitive. Our solution is based on the self-stabilizing construction of a data structure called the MIS Tree, a spanning tree of the network whose processes at even levels form a maximal indepen-dent set of the network. The MIS tree construction is the time bottleneck of our k-clustering algorithm, as it takes Î(n) rounds in the worst case, while the remainder of the algorithm takes O(D) rounds, where D is the diameter of the network. We would like to improve that time to be O(D), but we show that our distributed MIS tree construction is a P-complete problem
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
Species clustering in competitive Lotka-Volterra models
We study the properties of Lotka-Volterra competitive models in which the
intensity of the interaction among species depends on their position along an
abstract niche space through a competition kernel. We show analytically and
numerically that the properties of these models change dramatically when the
Fourier transform of this kernel is not positive definite, due to a pattern
forming instability. We estimate properties of the species distributions, such
as the steady number of species and their spacings, for different types of
kernels.Comment: 4 pages, 3 figure
The Clumping Transition in Niche Competition: a Robust Critical Phenomenon
We show analytically and numerically that the appearance of lumps and gaps in
the distribution of n competing species along a niche axis is a robust
phenomenon whenever the finiteness of the niche space is taken into account. In
this case depending if the niche width of the species is above or
below a threshold , which for large n coincides with 2/n, there are
two different regimes. For the lumpy pattern emerges
directly from the dominant eigenvector of the competition matrix because its
corresponding eigenvalue becomes negative. For the lumpy
pattern disappears. Furthermore, this clumping transition exhibits critical
slowing down as is approached from above. We also find that the number
of lumps of species vs. displays a stair-step structure. The positions
of these steps are distributed according to a power-law. It is thus
straightforward to predict the number of groups that can be packed along a
niche axis and it coincides with field measurements for a wide range of the
model parameters.Comment: 16 pages, 7 figures;
http://iopscience.iop.org/1742-5468/2010/05/P0500
Self-stabilizing k-clustering in mobile ad hoc networks
In this thesis, two silent self-stabilizing asynchronous distributed algorithms are given for constructing a k-clustering of a connected network of processes. These are the first self-stabilizing solutions to this problem. One algorithm, FLOOD, takes O( k) time and uses O(k log n) space per process, while the second algorithm, BFS-MIS-CLSTR, takes O(n) time and uses O(log n) space; where n is the size of the network. Processes have unique IDs, and there is no designated leader. BFS-MIS-CLSTR solves three problems; it elects a leader and constructs a BFS tree for the network, constructs a minimal independent set, and finally a k-clustering. Finding a minimal k-clustering is known to be NP -hard. If the network is a unit disk graph in a plane, BFS-MIS-CLSTR is within a factor of O(7.2552k) of choosing the minimal number of clusters; A lower bound is given, showing that any comparison-based algorithm for the k-clustering problem that takes o( diam) rounds has very bad worst case performance; Keywords: BFS tree construction, K-clustering, leader election, MIS construction, self-stabilization, unit disk graph
Opinion Dynamics in Social Networks with Hostile Camps: Consensus vs. Polarization
Most of the distributed protocols for multi-agent consensus assume that the
agents are mutually cooperative and "trustful," and so the couplings among the
agents bring the values of their states closer. Opinion dynamics in social
groups, however, require beyond these conventional models due to ubiquitous
competition and distrust between some pairs of agents, which are usually
characterized by repulsive couplings and may lead to clustering of the
opinions. A simple yet insightful model of opinion dynamics with both
attractive and repulsive couplings was proposed recently by C. Altafini, who
examined first-order consensus algorithms over static signed graphs. This
protocol establishes modulus consensus, where the opinions become the same in
modulus but may differ in signs. In this paper, we extend the modulus consensus
model to the case where the network topology is an arbitrary time-varying
signed graph and prove reaching modulus consensus under mild sufficient
conditions of uniform connectivity of the graph. For cut-balanced graphs, not
only sufficient, but also necessary conditions for modulus consensus are given.Comment: scheduled for publication in IEEE Transactions on Automatic Control,
2016, vol. 61, no. 7 (accepted in August 2015
Translucent windows: How uncertainty in competitive interactions impacts detection of community pattern
Trait variation and similarity among coexisting species can provide a window
into the mechanisms that maintain their coexistence. Recent theoretical
explorations suggest that competitive interactions will lead to groups, or
clusters, of species with similar traits. However, theoretical predictions
typically assume complete knowledge of the map between competition and measured
traits. These assumptions limit the plausible application of these patterns for
inferring competitive interactions in nature. Here we relax these restrictions
and find that the clustering pattern is robust to contributions of unknown or
unobserved niche axes. However, it may not be visible unless measured traits
are close proxies for niche strategies. We conclude that patterns along single
niche axes may reveal properties of interspecific competition in nature, but
detecting these patterns requires natural history expertise firmly tying traits
to niches.Comment: Main text: 18 pages, 6 figures. Appendices: A-G, 6 supplementary
figures. This is the peer reviewed version of the article of the same title
which has been accepted for publication at Ecology Letters. This article may
be used for non-commercial purposes in accordance with Wiley Terms and
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