1,362 research outputs found
Multiple domination models for placement of electric vehicle charging stations in road networks
Electric and hybrid vehicles play an increasing role in the road transport
networks. Despite their advantages, they have a relatively limited cruising
range in comparison to traditional diesel/petrol vehicles, and require
significant battery charging time. We propose to model the facility location
problem of the placement of charging stations in road networks as a multiple
domination problem on reachability graphs. This model takes into consideration
natural assumptions such as a threshold for remaining battery load, and
provides some minimal choice for a travel direction to recharge the battery.
Experimental evaluation and simulations for the proposed facility location
model are presented in the case of real road networks corresponding to the
cities of Boston and Dublin.Comment: 20 pages, 5 figures; Original version from March-April 201
Probabilistic Fair Clustering
In clustering problems, a central decision-maker is given a complete metric
graph over vertices and must provide a clustering of vertices that minimizes
some objective function. In fair clustering problems, vertices are endowed with
a color (e.g., membership in a group), and the features of a valid clustering
might also include the representation of colors in that clustering. Prior work
in fair clustering assumes complete knowledge of group membership. In this
paper, we generalize prior work by assuming imperfect knowledge of group
membership through probabilistic assignments. We present clustering algorithms
in this more general setting with approximation ratio guarantees. We also
address the problem of "metric membership", where different groups have a
notion of order and distance. Experiments are conducted using our proposed
algorithms as well as baselines to validate our approach and also surface
nuanced concerns when group membership is not known deterministically
Local Tomography of Large Networks under the Low-Observability Regime
This article studies the problem of reconstructing the topology of a network
of interacting agents via observations of the state-evolution of the agents. We
focus on the large-scale network setting with the additional constraint of
observations, where only a small fraction of the agents can be
feasibly observed. The goal is to infer the underlying subnetwork of
interactions and we refer to this problem as . In order to
study the large-scale setting, we adopt a proper stochastic formulation where
the unobserved part of the network is modeled as an Erd\"{o}s-R\'enyi random
graph, while the observable subnetwork is left arbitrary. The main result of
this work is establishing that, under this setting, local tomography is
actually possible with high probability, provided that certain conditions on
the network model are met (such as stability and symmetry of the network
combination matrix). Remarkably, such conclusion is established under the
- , where the cardinality of the observable
subnetwork is fixed, while the size of the overall network scales to infinity.Comment: To appear in IEEE Transactions on Information Theor
Optimal spatial transportation networks where link-costs are sublinear in link-capacity
Consider designing a transportation network on vertices in the plane,
with traffic demand uniform over all source-destination pairs. Suppose the cost
of a link of length and capacity scales as for fixed
. Under appropriate standardization, the cost of the minimum cost
Gilbert network grows essentially as , where on and on . This quantity is an upper bound in
the worst case (of vertex positions), and a lower bound under mild regularity
assumptions. Essentially the same bounds hold if we constrain the network to be
efficient in the sense that average route-length is only times
average straight line length. The transition at corresponds to
the dominant cost contribution changing from short links to long links. The
upper bounds arise in the following type of hierarchical networks, which are
therefore optimal in an order of magnitude sense. On the large scale, use a
sparse Poisson line process to provide long-range links. On the medium scale,
use hierachical routing on the square lattice. On the small scale, link
vertices directly to medium-grid points. We discuss one of many possible
variant models, in which links also have a designed maximum speed and the
cost becomes .Comment: 13 page
Connectivity vs Capacity in Dense Ad Hoc Networks
We study the connectivity and capacity of finite area ad hoc wireless networks, with an increasing number of nodes (dense networks). We find that the properties of the network strongly depend on the shape of the attenuation function. For power law attenuation functions, connectivity scales, and the available rate per node is known to decrease like 1/sqrt(n). On the contrary, if the attenuation function does not have a singularity at the origin and is uniformly bounded, we obtain bounds on the percolation domain for large node densities, which show that either the network becomes disconnected, or the available rate per node decreases like 1/n
Maximal stream and minimal cutset for first passage percolation through a domain of
We consider the standard first passage percolation model in the rescaled
graph for and a domain of boundary
in . Let and be two disjoint open subsets
of , representing the parts of through which some water can
enter and escape from . A law of large numbers for the maximal flow
from to in is already known. In this paper we
investigate the asymptotic behavior of a maximal stream and a minimal cutset. A
maximal stream is a vector measure that describes how the
maximal amount of fluid can cross . Under conditions on the regularity
of the domain and on the law of the capacities of the edges, we prove that the
sequence converges a.s. to the set of the
solutions of a continuous deterministic problem of maximal stream in an
anisotropic network. A minimal cutset can been seen as the boundary of a set
that separates from in and whose
random capacity is minimal. Under the same conditions, we prove that the
sequence converges toward the set of the solutions of a
continuous deterministic problem of minimal cutset. We deduce from this a
continuous deterministic max-flow min-cut theorem and a new proof of the law of
large numbers for the maximal flow. This proof is more natural than the
existing one, since it relies on the study of maximal streams and minimal
cutsets, which are the pertinent objects to look at.Comment: Published in at http://dx.doi.org/10.1214/13-AOP851 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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