5,074 research outputs found
Embedding Graphs under Centrality Constraints for Network Visualization
Visual rendering of graphs is a key task in the mapping of complex network
data. Although most graph drawing algorithms emphasize aesthetic appeal,
certain applications such as travel-time maps place more importance on
visualization of structural network properties. The present paper advocates two
graph embedding approaches with centrality considerations to comply with node
hierarchy. The problem is formulated first as one of constrained
multi-dimensional scaling (MDS), and it is solved via block coordinate descent
iterations with successive approximations and guaranteed convergence to a KKT
point. In addition, a regularization term enforcing graph smoothness is
incorporated with the goal of reducing edge crossings. A second approach
leverages the locally-linear embedding (LLE) algorithm which assumes that the
graph encodes data sampled from a low-dimensional manifold. Closed-form
solutions to the resulting centrality-constrained optimization problems are
determined yielding meaningful embeddings. Experimental results demonstrate the
efficacy of both approaches, especially for visualizing large networks on the
order of thousands of nodes.Comment: Submitted to IEEE Transactions on Visualization and Computer Graphic
Plausible Mobility: Inferring Movement from Contacts
We address the difficult question of inferring plausible node mobility based
only on information from wireless contact traces. Working with mobility
information allows richer protocol simulations, particularly in dense networks,
but requires complex set-ups to measure, whereas contact information is easier
to measure but only allows for simplistic simulation models. In a contact trace
a lot of node movement information is irretrievably lost so the original
positions and velocities are in general out of reach. We propose a fast
heuristic algorithm, inspired by dynamic force-based graph drawing, capable of
inferring a plausible movement from any contact trace, and evaluate it on both
synthetic and real-life contact traces. Our results reveal that (i) the quality
of the inferred mobility is directly linked to the precision of the measured
contact trace, and (ii) the simple addition of appropriate anticipation forces
between nodes leads to an accurate inferred mobility.Comment: 8 pages, 8 figures, 1 tabl
05361 Abstracts Collection -- Algorithmic Aspects of Large and Complex Networks
From 04.09.05 to 09.09.05, the Dagstuhl Seminar 05361 ``Algorithmic Aspects of Large and Complex Networks\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Distributed Detection and Estimation in Wireless Sensor Networks
In this article we consider the problems of distributed detection and
estimation in wireless sensor networks. In the first part, we provide a general
framework aimed to show how an efficient design of a sensor network requires a
joint organization of in-network processing and communication. Then, we recall
the basic features of consensus algorithm, which is a basic tool to reach
globally optimal decisions through a distributed approach. The main part of the
paper starts addressing the distributed estimation problem. We show first an
entirely decentralized approach, where observations and estimations are
performed without the intervention of a fusion center. Then, we consider the
case where the estimation is performed at a fusion center, showing how to
allocate quantization bits and transmit powers in the links between the nodes
and the fusion center, in order to accommodate the requirement on the maximum
estimation variance, under a constraint on the global transmit power. We extend
the approach to the detection problem. Also in this case, we consider the
distributed approach, where every node can achieve a globally optimal decision,
and the case where the decision is taken at a central node. In the latter case,
we show how to allocate coding bits and transmit power in order to maximize the
detection probability, under constraints on the false alarm rate and the global
transmit power. Then, we generalize consensus algorithms illustrating a
distributed procedure that converges to the projection of the observation
vector onto a signal subspace. We then address the issue of energy consumption
in sensor networks, thus showing how to optimize the network topology in order
to minimize the energy necessary to achieve a global consensus. Finally, we
address the problem of matching the topology of the network to the graph
describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R.
Chellapa and S. Theodoridis, Eds., Elsevier, 201
Combinatorial Optimization
This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th
Multilevel Methods for Sparsification and Linear Arrangement Problems on Networks
The computation of network properties such as diameter, centrality indices, and paths on networks may become a major bottleneck in the analysis of network if the network is large. Scalable approximation algorithms, heuristics and structure preserving network sparsification methods play an important role in modern network analysis. In the first part of this thesis, we develop a robust network sparsification method that enables filtering of either, so called, long- and short-range edges or both. Edges are first ranked by their algebraic distances and then sampled. Furthermore, we also combine this method with a multilevel framework to provide a multilevel sparsification framework that can control the sparsification process at different coarse-grained resolutions. Experimental results demonstrate an effectiveness of the proposed methods without significant loss in a quality of computed network properties. In the second part of the thesis, we introduce asymmetric coarsening schemes for multilevel algorithms developed for linear arrangement problems. Effectiveness of the set of coarse variables, and the corresponding interpolation matrix is the central problem in any multigrid algorithm. We are pushing the boundaries of fast maximum weighted matching algorithms for coarsening schemes on graphs by introducing novel ideas for asymmetric coupling between coarse and fine variables of the problem
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