2,408 research outputs found
Graphs with large generalized (edge-)connectivity
The generalized -connectivity of a graph , introduced by
Hager in 1985, is a nice generalization of the classical connectivity.
Recently, as a natural counterpart, we proposed the concept of generalized
-edge-connectivity . In this paper, graphs of order such
that and for even
are characterized.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1207.183
The generalized 3-connectivity of Lexicographic product graphs
The generalized -connectivity of a graph , introduced by
Chartrand et al., is a natural and nice generalization of the concept of
(vertex-)connectivity. In this paper, we prove that for any two connected
graphs and , . We also give
upper bounds for and . Moreover, all
the bounds are sharp.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1103.609
The strong rainbow vertex-connection of graphs
A vertex-colored graph is said to be rainbow vertex-connected if every
two vertices of are connected by a path whose internal vertices have
distinct colors, such a path is called a rainbow path. The rainbow
vertex-connection number of a connected graph , denoted by , is the
smallest number of colors that are needed in order to make rainbow
vertex-connected. If for every pair of distinct vertices, contains a
rainbow geodesic, then is strong rainbow vertex-connected. The
minimum number for which there exists a -vertex-coloring of that
results in a strongly rainbow vertex-connected graph is called the strong
rainbow vertex-connection number of , denoted by . Observe that
for any nontrivial connected graph . In this paper,
sharp upper and lower bounds of are given for a connected graph
of order , that is, . Graphs of order such that
are characterized, respectively. It is also shown that,
for each pair of integers with and , there
exists a connected graph such that and .Comment: 10 page
Enabling Multi-level Trust in Privacy Preserving Data Mining
Privacy Preserving Data Mining (PPDM) addresses the problem of developing
accurate models about aggregated data without access to precise information in
individual data record. A widely studied \emph{perturbation-based PPDM}
approach introduces random perturbation to individual values to preserve
privacy before data is published. Previous solutions of this approach are
limited in their tacit assumption of single-level trust on data miners.
In this work, we relax this assumption and expand the scope of
perturbation-based PPDM to Multi-Level Trust (MLT-PPDM). In our setting, the
more trusted a data miner is, the less perturbed copy of the data it can
access. Under this setting, a malicious data miner may have access to
differently perturbed copies of the same data through various means, and may
combine these diverse copies to jointly infer additional information about the
original data that the data owner does not intend to release. Preventing such
\emph{diversity attacks} is the key challenge of providing MLT-PPDM services.
We address this challenge by properly correlating perturbation across copies at
different trust levels. We prove that our solution is robust against diversity
attacks with respect to our privacy goal. That is, for data miners who have
access to an arbitrary collection of the perturbed copies, our solution prevent
them from jointly reconstructing the original data more accurately than the
best effort using any individual copy in the collection. Our solution allows a
data owner to generate perturbed copies of its data for arbitrary trust levels
on-demand. This feature offers data owners maximum flexibility.Comment: 20 pages, 5 figures. Accepted for publication in IEEE Transactions on
Knowledge and Data Engineerin
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