6,596 research outputs found
Minimum congestion spanning trees in planar graphs
The main purpose of the paper is to develop an approach to evaluation or
estimation of the spanning tree congestion of planar graphs. This approach is
used to evaluate the spanning tree congestion of triangular grids
Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes
We investigate approximating joint distributions of random processes with
causal dependence tree distributions. Such distributions are particularly
useful in providing parsimonious representation when there exists causal
dynamics among processes. By extending the results by Chow and Liu on
dependence tree approximations, we show that the best causal dependence tree
approximation is the one which maximizes the sum of directed informations on
its edges, where best is defined in terms of minimizing the KL-divergence
between the original and the approximate distribution. Moreover, we describe a
low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure
A note on the data-driven capacity of P2P networks
We consider two capacity problems in P2P networks. In the first one, the
nodes have an infinite amount of data to send and the goal is to optimally
allocate their uplink bandwidths such that the demands of every peer in terms
of receiving data rate are met. We solve this problem through a mapping from a
node-weighted graph featuring two labels per node to a max flow problem on an
edge-weighted bipartite graph. In the second problem under consideration, the
resource allocation is driven by the availability of the data resource that the
peers are interested in sharing. That is a node cannot allocate its uplink
resources unless it has data to transmit first. The problem of uplink bandwidth
allocation is then equivalent to constructing a set of directed trees in the
overlay such that the number of nodes receiving the data is maximized while the
uplink capacities of the peers are not exceeded. We show that the problem is
NP-complete, and provide a linear programming decomposition decoupling it into
a master problem and multiple slave subproblems that can be resolved in
polynomial time. We also design a heuristic algorithm in order to compute a
suboptimal solution in a reasonable time. This algorithm requires only a local
knowledge from nodes, so it should support distributed implementations.
We analyze both problems through a series of simulation experiments featuring
different network sizes and network densities. On large networks, we compare
our heuristic and its variants with a genetic algorithm and show that our
heuristic computes the better resource allocation. On smaller networks, we
contrast these performances to that of the exact algorithm and show that
resource allocation fulfilling a large part of the peer can be found, even for
hard configuration where no resources are in excess.Comment: 10 pages, technical report assisting a submissio
On the Properties of Gromov Matrices and their Applications in Network Inference
The spanning tree heuristic is a commonly adopted procedure in network
inference and estimation. It allows one to generalize an inference method
developed for trees, which is usually based on a statistically rigorous
approach, to a heuristic procedure for general graphs by (usually randomly)
choosing a spanning tree in the graph to apply the approach developed for
trees. However, there are an intractable number of spanning trees in a dense
graph. In this paper, we represent a weighted tree with a matrix, which we call
a Gromov matrix. We propose a method that constructs a family of Gromov
matrices using convex combinations, which can be used for inference and
estimation instead of a randomly selected spanning tree. This procedure
increases the size of the candidate set and hence enhances the performance of
the classical spanning tree heuristic. On the other hand, our new scheme is
based on simple algebraic constructions using matrices, and hence is still
computationally tractable. We discuss some applications on network inference
and estimation to demonstrate the usefulness of the proposed method
The Knapsack Problem with Neighbour Constraints
We study a constrained version of the knapsack problem in which dependencies
between items are given by the adjacencies of a graph. In the 1-neighbour
knapsack problem, an item can be selected only if at least one of its
neighbours is also selected. In the all-neighbours knapsack problem, an item
can be selected only if all its neighbours are also selected. We give
approximation algorithms and hardness results when the nodes have both uniform
and arbitrary weight and profit functions, and when the dependency graph is
directed and undirected.Comment: Full version of IWOCA 2011 pape
Towards a Queueing-Based Framework for In-Network Function Computation
We seek to develop network algorithms for function computation in sensor
networks. Specifically, we want dynamic joint aggregation, routing, and
scheduling algorithms that have analytically provable performance benefits due
to in-network computation as compared to simple data forwarding. To this end,
we define a class of functions, the Fully-Multiplexible functions, which
includes several functions such as parity, MAX, and k th -order statistics. For
such functions we exactly characterize the maximum achievable refresh rate of
the network in terms of an underlying graph primitive, the min-mincut. In
acyclic wireline networks, we show that the maximum refresh rate is achievable
by a simple algorithm that is dynamic, distributed, and only dependent on local
information. In the case of wireless networks, we provide a MaxWeight-like
algorithm with dynamic flow splitting, which is shown to be throughput-optimal
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