2,423 research outputs found
Node Removal Vulnerability of the Largest Component of a Network
The connectivity structure of a network can be very sensitive to removal of
certain nodes in the network. In this paper, we study the sensitivity of the
largest component size to node removals. We prove that minimizing the largest
component size is equivalent to solving a matrix one-norm minimization problem
whose column vectors are orthogonal and sparse and they form a basis of the
null space of the associated graph Laplacian matrix. A greedy node removal
algorithm is then proposed based on the matrix one-norm minimization. In
comparison with other node centralities such as node degree and betweenness,
experimental results on US power grid dataset validate the effectiveness of the
proposed approach in terms of reduction of the largest component size with
relatively few node removals.Comment: Published in IEEE GlobalSIP 201
On Varieties of Ordered Automata
The Eilenberg correspondence relates varieties of regular languages to
pseudovarieties of finite monoids. Various modifications of this correspondence
have been found with more general classes of regular languages on one hand and
classes of more complex algebraic structures on the other hand. It is also
possible to consider classes of automata instead of algebraic structures as a
natural counterpart of classes of languages. Here we deal with the
correspondence relating positive -varieties of languages to
positive -varieties of ordered automata and we present various
specific instances of this correspondence. These bring certain well-known
results from a new perspective and also some new observations. Moreover,
complexity aspects of the membership problem are discussed both in the
particular examples and in a general setting
- …