4,996 research outputs found
Clustering with diversity
We consider the {\em clustering with diversity} problem: given a set of
colored points in a metric space, partition them into clusters such that each
cluster has at least points, all of which have distinct colors.
We give a 2-approximation to this problem for any when the objective
is to minimize the maximum radius of any cluster. We show that the
approximation ratio is optimal unless , by providing a matching
lower bound. Several extensions to our algorithm have also been developed for
handling outliers. This problem is mainly motivated by applications in
privacy-preserving data publication.Comment: Extended abstract accepted in ICALP 2010. Keywords: Approximation
algorithm, k-center, k-anonymity, l-diversit
Critical Phenomena in Head-on Collisions of Neutron Stars
We found type I critical collapses of compact objects modeled by a polytropic
equation of state (EOS) with polytropic index without the
ultra-relativistic assumption. The object is formed in head-on collisions of
neutron stars. Further we showed that the critical collapse can occur due to a
change of the EOS, without fine tuning of initial data. This opens the
possibility that a neutron star like compact object, not just those formed in a
collision, may undergo a critical collapse in processes which slowly change the
EOS, such as cooling.Comment: 4 pages,6 figures, 15 reference
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