6,079 research outputs found
Discrete-time multi-scale systems
We introduce multi-scale filtering by the way of certain double convolution
systems. We prove stability theorems for these systems and make connections
with function theory in the poly-disc. Finally, we compare the framework
developed here with the white noise space framework, within which a similar
class of double convolution systems has been defined earlier
Fast exact algorithms for some connectivity problems parametrized by clique-width
Given a clique-width -expression of a graph , we provide time algorithms for connectivity constraints on locally checkable properties
such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected
Vertex Cover. We also propose a time algorithm for Feedback
Vertex Set. The best running times for all the considered cases were either
or worse
Pontryagin principle for a Mayer problem governed by a delay functional differential equation
We establish Pontryagin principles for a Mayer's optimal control problem
governed by a functional differential equation. The control functions are
piecewise continuous and the state functions are piecewise continuously
differentiable. To do that, we follow the method created by Philippe Michel for
systems governed by ordinary differential equations, and we use properties of
the resolvent of a linear functional differential equation
More applications of the d-neighbor equivalence: acyclicity and connectivity constraints
In this paper, we design a framework to obtain efficient algorithms for
several problems with a global constraint (acyclicity or connectivity) such as
Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree,
Longest Induced Path, and Feedback Vertex Set. We design a meta-algorithm that
solves all these problems and whose running time is upper bounded by
, , and where is respectively the clique-width,
-rank-width, rank-width and maximum induced matching width of a
given decomposition. Our meta-algorithm simplifies and unifies the known
algorithms for each of the parameters and its running time matches
asymptotically also the running times of the best known algorithms for basic
NP-hard problems such as Vertex Cover and Dominating Set. Our framework is
based on the -neighbor equivalence defined in [Bui-Xuan, Telle and
Vatshelle, TCS 2013]. The results we obtain highlight the importance of this
equivalence relation on the algorithmic applications of width measures.
We also prove that our framework could be useful for -hard problems
parameterized by clique-width such as Max Cut and Maximum Minimal Cut. For
these latter problems, we obtain , and time
algorithms where is respectively the clique-width, the
-rank-width and the rank-width of the input graph
Euler-lagrange equation for a delay variational problem
We establish Euler-Lagrange equations for a problem of Calculus of variations
where the unknown variable contains a term of delay on a segment
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