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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
Self-dual Hopfions
We construct static and time-dependent exact soliton solutions with
non-trivial Hopf topological charge for a field theory in 3+1 dimensions with
the target space being the two dimensional sphere S**2. The model considered is
a reduction of the so-called extended Skyrme-Faddeev theory by the removal of
the quadratic term in derivatives of the fields. The solutions are constructed
using an ansatz based on the conformal and target space symmetries. The
solutions are said self-dual because they solve first order differential
equations which together with some conditions on the coupling constants, imply
the second order equations of motion. The solutions belong to a sub-sector of
the theory with an infinite number of local conserved currents. The equation
for the profile function of the ansatz corresponds to the Bogomolny equation
for the sine-Gordon model.Comment: plain latex, no figures, 23 page
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