174,452 research outputs found
Complex network classification using partially self-avoiding deterministic walks
Complex networks have attracted increasing interest from various fields of
science. It has been demonstrated that each complex network model presents
specific topological structures which characterize its connectivity and
dynamics. Complex network classification rely on the use of representative
measurements that model topological structures. Although there are a large
number of measurements, most of them are correlated. To overcome this
limitation, this paper presents a new measurement for complex network
classification based on partially self-avoiding walks. We validate the
measurement on a data set composed by 40.000 complex networks of four
well-known models. Our results indicate that the proposed measurement improves
correct classification of networks compared to the traditional ones
Design and Analysis of Distributed Averaging with Quantized Communication
Consider a network whose nodes have some initial values, and it is desired to
design an algorithm that builds on neighbor to neighbor interactions with the
ultimate goal of convergence to the average of all initial node values or to
some value close to that average. Such an algorithm is called generically
"distributed averaging," and our goal in this paper is to study the performance
of a subclass of deterministic distributed averaging algorithms where the
information exchange between neighboring nodes (agents) is subject to uniform
quantization. With such quantization, convergence to the precise average cannot
be achieved in general, but the convergence would be to some value close to it,
called quantized consensus. Using Lyapunov stability analysis, we characterize
the convergence properties of the resulting nonlinear quantized system. We show
that in finite time and depending on initial conditions, the algorithm will
either cause all agents to reach a quantized consensus where the consensus
value is the largest quantized value not greater than the average of their
initial values, or will lead all variables to cycle in a small neighborhood
around the average. In the latter case, we identify tight bounds for the size
of the neighborhood and we further show that the error can be made arbitrarily
small by adjusting the algorithm's parameters in a distributed manner
Faster Parametric Shortest Path and Minimum Balance Algorithms
The parametric shortest path problem is to find the shortest paths in graph
where the edge costs are of the form w_ij+lambda where each w_ij is constant
and lambda is a parameter that varies. The problem is to find shortest path
trees for every possible value of lambda.
The minimum-balance problem is to find a ``weighting'' of the vertices so
that adjusting the edge costs by the vertex weights yields a graph in which,
for every cut, the minimum weight of any edge crossing the cut in one direction
equals the minimum weight of any edge crossing the cut in the other direction.
The paper presents fast algorithms for both problems. The algorithms run in
O(nm+n^2 log n) time. The paper also describes empirical studies of the
algorithms on random graphs, suggesting that the expected time for finding a
minimum-mean cycle (an important special case of both problems) is O(n log(n) +
m)
Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions
We consider the general problem of finding the minimum weight \bm-matching
on arbitrary graphs. We prove that, whenever the linear programming (LP)
relaxation of the problem has no fractional solutions, then the belief
propagation (BP) algorithm converges to the correct solution. We also show that
when the LP relaxation has a fractional solution then the BP algorithm can be
used to solve the LP relaxation. Our proof is based on the notion of graph
covers and extends the analysis of (Bayati-Shah-Sharma 2005 and Huang-Jebara
2007}.
These results are notable in the following regards: (1) It is one of a very
small number of proofs showing correctness of BP without any constraint on the
graph structure. (2) Variants of the proof work for both synchronous and
asynchronous BP; it is the first proof of convergence and correctness of an
asynchronous BP algorithm for a combinatorial optimization problem.Comment: 28 pages, 2 figures. Submitted to SIAM journal on Discrete
Mathematics on March 19, 2009; accepted for publication (in revised form)
August 30, 2010; published electronically July 1, 201
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