61,870 research outputs found
The -matching problem on bipartite graphs
The -matching problem on bipartite graphs is studied with a local
algorithm. A -matching () on a bipartite graph is a set of matched
edges, in which each vertex of one type is adjacent to at most matched edge
and each vertex of the other type is adjacent to at most matched edges. The
-matching problem on a given bipartite graph concerns finding -matchings
with the maximum size. Our approach to this combinatorial optimization are of
two folds. From an algorithmic perspective, we adopt a local algorithm as a
linear approximate solver to find -matchings on general bipartite graphs,
whose basic component is a generalized version of the greedy leaf removal
procedure in graph theory. From an analytical perspective, in the case of
random bipartite graphs with the same size of two types of vertices, we develop
a mean-field theory for the percolation phenomenon underlying the local
algorithm, leading to a theoretical estimation of -matching sizes on
coreless graphs. We hope that our results can shed light on further study on
algorithms and computational complexity of the optimization problem.Comment: 15 pages, 3 figure
Pion Production in Heavy-ion Collisions in the 1 A GeV region
Within the framework of the improved isospin dependent quantum molecular
dynamics (ImIQMD) model, the pion emission in heavy-ion collisions in the
region 1 A GeV is investigated systematically, in which the pion is considered
to be mainly produced by the decay of resonances (1232) and
N*(1440). The in-medium dependence and Coulomb effects of the pion production
are included in the calculation. Total pion multiplicity and
yields are calculated for the reaction Au+Au in central
collisions for selected Skyrme parameters SkP, SLy6, Ska, SIII and compared
them with the measured data by the FOPI collaboration.Comment: 9 pages, 5 figure
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