15 research outputs found
Ranking by Loops: a new approach to categorization
We introduce Loop Ranking, a new ranking measure based on the detection of
closed paths, which can be computed in an efficient way. We analyze it with
respect to several ranking measures which have been proposed in the past, and
are widely used to capture the relative importance of the vertices in complex
networks. We argue that Loop Ranking is a very appropriate measure to quantify
the role of both vertices and edges in the network traffic.Comment: 4 pages, 2 figures, 1 table, corrected misprin
Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries
We propose an efficient framework for enabling secure multi-party numerical
computations in a Peer-to-Peer network. This problem arises in a range of
applications such as collaborative filtering, distributed computation of trust
and reputation, monitoring and other tasks, where the computing nodes is
expected to preserve the privacy of their inputs while performing a joint
computation of a certain function. Although there is a rich literature in the
field of distributed systems security concerning secure multi-party
computation, in practice it is hard to deploy those methods in very large scale
Peer-to-Peer networks. In this work, we try to bridge the gap between
theoretical algorithms in the security domain, and a practical Peer-to-Peer
deployment.
We consider two security models. The first is the semi-honest model where
peers correctly follow the protocol, but try to reveal private information. We
provide three possible schemes for secure multi-party numerical computation for
this model and identify a single light-weight scheme which outperforms the
others. Using extensive simulation results over real Internet topologies, we
demonstrate that our scheme is scalable to very large networks, with up to
millions of nodes. The second model we consider is the malicious peers model,
where peers can behave arbitrarily, deliberately trying to affect the results
of the computation as well as compromising the privacy of other peers. For this
model we provide a fourth scheme to defend the execution of the computation
against the malicious peers. The proposed scheme has a higher complexity
relative to the semi-honest model. Overall, we provide the Peer-to-Peer network
designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA)
200
Fermions and Loops on Graphs. I. Loop Calculus for Determinant
This paper is the first in the series devoted to evaluation of the partition
function in statistical models on graphs with loops in terms of the
Berezin/fermion integrals. The paper focuses on a representation of the
determinant of a square matrix in terms of a finite series, where each term
corresponds to a loop on the graph. The representation is based on a fermion
version of the Loop Calculus, previously introduced by the authors for
graphical models with finite alphabets. Our construction contains two levels.
First, we represent the determinant in terms of an integral over anti-commuting
Grassman variables, with some reparametrization/gauge freedom hidden in the
formulation. Second, we show that a special choice of the gauge, called BP
(Bethe-Peierls or Belief Propagation) gauge, yields the desired loop
representation. The set of gauge-fixing BP conditions is equivalent to the
Gaussian BP equations, discussed in the past as efficient (linear scaling)
heuristics for estimating the covariance of a sparse positive matrix.Comment: 11 pages, 1 figure; misprints correcte
Optimal Location of Sources in Transportation Networks
We consider the problem of optimizing the locations of source nodes in
transportation networks. A reduction of the fraction of surplus nodes induces a
glassy transition. In contrast to most constraint satisfaction problems
involving discrete variables, our problem involves continuous variables which
lead to cavity fields in the form of functions. The one-step replica symmetry
breaking (1RSB) solution involves solving a stable distribution of functionals,
which is in general infeasible. In this paper, we obtain small closed sets of
functional cavity fields and demonstrate how functional recursions are
converted to simple recursions of probabilities, which make the 1RSB solution
feasible. The physical results in the replica symmetric (RS) and the 1RSB
frameworks are thus derived and the stability of the RS and 1RSB solutions are
examined.Comment: 38 pages, 18 figure
Spectral Theory of Sparse Non-Hermitian Random Matrices
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matrices provide crucial information on system
stability and susceptibility, however, their study is greatly complicated by
the twin challenges of a lack of symmetry and a sparse interaction structure.
In this review we provide a concise and systematic introduction to the main
tools and results in this field. We show how the spectra of sparse
non-Hermitian matrices can be computed via an analogy with infinite dimensional
operators obeying certain recursion relations. With reference to three
illustrative examples --- adjacency matrices of regular oriented graphs,
adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency
matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the
use of these methods to obtain both analytic and numerical results for the
spectrum, the spectral distribution, the location of outlier eigenvalues, and
the statistical properties of eigenvectors.Comment: 60 pages, 10 figure
Efficient Large Scale Content Distribution
This paper considers the problem of supporting high-bandwidth, scalable application level multicast. It provides a formal treatment of the problem which takes into consideration network distances. It presents the Julia locality-aware content dissemination scheme, a highly efficient and fast method whose distribution is both time-aware and proximity-aware. A formal comparison of Julia with several reference protocols is given
Practical locality-awareness for large scale information sharing
Tulip is an overlay for routing, searching and publish-lookup information sharing. It offers a unique combination of the advantages of both structured and unstructured overlays, that does not co-exist in any previous solution. Tulip features locality awareness (stretch 2) and fault tolerance (nodes can route around failures). It supports under the same roof exact keyed-lookup, nearest, copy location, and global information search. Tulip has been deployed and its locality and fault tolerance properties verified over a real wide-area network