7,006 research outputs found
Next Generation Cluster Editing
This work aims at improving the quality of structural variant prediction from
the mapped reads of a sequenced genome. We suggest a new model based on cluster
editing in weighted graphs and introduce a new heuristic algorithm that allows
to solve this problem quickly and with a good approximation on the huge graphs
that arise from biological datasets
Degrees and distances in random and evolving Apollonian networks
This paper studies Random and Evolving Apollonian networks (RANs and EANs),
in d dimension for any d>=2, i.e. dynamically evolving random d dimensional
simplices looked as graphs inside an initial d-dimensional simplex. We
determine the limiting degree distribution in RANs and show that it follows a
power law tail with exponent tau=(2d-1)/(d-1). We further show that the degree
distribution in EANs converges to the same degree distribution if the
simplex-occupation parameter in the n-th step of the dynamics is q_n->0 and
sum_{n=0}^infty q_n =infty. This result gives a rigorous proof for the
conjecture of Zhang et al. that EANs tend to show similar behavior as RANs once
the occupation parameter q->0. We also determine the asymptotic behavior of
shortest paths in RANs and EANs for arbitrary d dimensions. For RANs we show
that the shortest path between two uniformly chosen vertices (typical
distance), the flooding time of a uniformly picked vertex and the diameter of
the graph after n steps all scale as constant times log n. We determine the
constants for all three cases and prove a central limit theorem for the typical
distances. We prove a similar CLT for typical distances in EANs
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