8,886 research outputs found
Local heuristics and the emergence of spanning subgraphs in complex networks
We study the use of local heuristics to determine spanning subgraphs for use
in the dissemination of information in complex networks. We introduce two
different heuristics and analyze their behavior in giving rise to spanning
subgraphs that perform well in terms of allowing every node of the network to
be reached, of requiring relatively few messages and small node bandwidth for
information dissemination, and also of stretching paths with respect to the
underlying network only modestly. We contribute a detailed mathematical
analysis of one of the heuristics and provide extensive simulation results on
random graphs for both of them. These results indicate that, within certain
limits, spanning subgraphs are indeed expected to emerge that perform well in
respect to all requirements. We also discuss the spanning subgraphs' inherent
resilience to failures and adaptability to topological changes
Probabilistic heuristics for disseminating information in networks
We study the problem of disseminating a piece of information through all the
nodes of a network, given that it is known originally only to a single node. In
the absence of any structural knowledge on the network other than the nodes'
neighborhoods, this problem is traditionally solved by flooding all the
network's edges. We analyze a recently introduced probabilistic algorithm for
flooding and give an alternative probabilistic heuristic that can lead to some
cost-effective improvements, like better trade-offs between the message and
time complexities involved. We analyze the two algorithms both mathematically
and by means of simulations, always within a random-graph framework and
considering relevant node-degree distributions
Topics in Born-Infeld Electrodynamics
Classical version of Born-Infeld electrodynamics is recalled and its most
important properties discussed. Then we analyze possible abelian and
non-abelian generalizations of this theory, and show how certain soliton-like
configurations can be obtained. The relationship with the Standard Model of
electroweak interactions is also mentioned.Comment: (One new reference added). 15 pages, LaTeX. To be published in the
Proceedings of XXXVII Karpacz Winter School edited in the Proceedings Series
of American Mathematical Society, editors J. Lukierski and J. Rembielinsk
Two novel evolutionary formulations of the graph coloring problem
We introduce two novel evolutionary formulations of the problem of coloring
the nodes of a graph. The first formulation is based on the relationship that
exists between a graph's chromatic number and its acyclic orientations. It
views such orientations as individuals and evolves them with the aid of
evolutionary operators that are very heavily based on the structure of the
graph and its acyclic orientations. The second formulation, unlike the first
one, does not tackle one graph at a time, but rather aims at evolving a
`program' to color all graphs belonging to a class whose members all have the
same number of nodes and other common attributes. The heuristics that result
from these formulations have been tested on some of the Second DIMACS
Implementation Challenge benchmark graphs, and have been found to be
competitive when compared to the several other heuristics that have also been
tested on those graphs.Comment: To appear in Journal of Combinatorial Optimizatio
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