330 research outputs found
More Applications of the d-Neighbor Equivalence: Connectivity and Acyclicity 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. For all these problems, we obtain 2^O(k)* n^O(1), 2^O(k log(k))* n^O(1), 2^O(k^2) * n^O(1) and n^O(k) time algorithms parameterized respectively by clique-width, Q-rank-width, rank-width and maximum induced matching width. Our approach simplifies and unifies the known algorithms for each of the parameters and match asymptotically also the running time of the best algorithms for basic NP-hard problems such as Vertex Cover and Dominating Set. Our framework is based on the d-neighbor equivalence defined in [Bui-Xuan, Telle and Vatshelle, TCS 2013]. The results we obtain highlight the importance and the generalizing power of this equivalence relation on width measures. We also prove that this equivalence relation could be useful for Max Cut: a W[1]-hard problem parameterized by clique-width. For this latter problem, we obtain n^O(k), n^O(k) and n^(2^O(k)) time algorithm parameterized by clique-width, Q-rank-width and rank-width
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
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
Non-Poisson statistics of settling spheres
International audienceDirect tracking of the particle positions in a sedimenting suspension indicates that the particles are not simply randomly distributed. The initial mixing of the suspension leads to a microstructure which consists of regions devoid of particles surrounded by regions where particles have an excess of close neighbors and which is maintained during sedimentation
Tight Lower Bounds for Problems Parameterized by Rank-Width
We show that there is no 2o(k2)nO(1) time algorithm for Independent Set on n-vertex graphs with rank-width k, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the 2O(k2)nO(1) time algorithm given by Bui-Xuan, Telle, and Vatshelle [Discret. Appl. Math., 2010] and it answers the open question of Bergougnoux and Kanté [SIAM J. Discret. Math., 2021]. We also show that the known 2O(k2)nO(1) time algorithms for Weighted Dominating Set, Maximum Induced Matching and Feedback Vertex Set parameterized by rank-width k are optimal assuming ETH. Our results are the first tight ETH lower bounds parameterized by rank-width that do not follow directly from lower bounds for n-vertex graphs
New Width Parameters for Independent Set: One-sided-mim-width and Neighbor-depth
We study the tractability of the maximum independent set problem from the
viewpoint of graph width parameters, with the goal of defining a width
parameter that is as general as possible and allows to solve independent set in
polynomial-time on graphs where the parameter is bounded. We introduce two new
graph width parameters: one-sided maximum induced matching-width (o-mim-width)
and neighbor-depth. O-mim-width is a graph parameter that is more general than
the known parameters mim-width and tree-independence number, and we show that
independent set and feedback vertex set can be solved in polynomial-time given
a decomposition with bounded o-mim-width. O-mim-width is the first width
parameter that gives a common generalization of chordal graphs and graphs of
bounded clique-width in terms of tractability of these problems.
The parameter o-mim-width, as well as the related parameters mim-width and
sim-width, have the limitation that no algorithms are known to compute
bounded-width decompositions in polynomial-time. To partially resolve this
limitation, we introduce the parameter neighbor-depth. We show that given a
graph of neighbor-depth , independent set can be solved in time
even without knowing a corresponding decomposition. We also show that
neighbor-depth is bounded by a polylogarithmic function on the number of
vertices on large classes of graphs, including graphs of bounded o-mim-width,
and more generally graphs of bounded sim-width, giving a quasipolynomial-time
algorithm for independent set on these graph classes. This resolves an open
problem asked by Kang, Kwon, Str{\o}mme, and Telle [TCS 2017].Comment: 26 pages, 1 figure. This is the full version of an extended abstract
that will appear in WG202
Une démarche pour l'enseignement des réseaux et de la communication
Cet article se propose de faire le point sur l'enseignement de l'informatique dans le domaine des réseaux. Il s'appuie sur nos expériences pédagogiques post-baccalauréat dans les filiÚres informatiques ( BTS, IUT, MIAG, MAITRISE, DEA, DESS... ).Nous décrivons dans une premiÚre partie le « concept réseau » et son rÎle prépondérant dans l'informatique d'aujourd'hui. Face aux problÚmes posés par ce domaine complexe, nous énonçons quelques « rÚgles d'or » pour une approche progressive et applicative conduisant à expérimenter des systÚmes de communications locaux.Nous exposons notre démarche didactique pour l'une des rÚgles énoncées : « Apprendre la communication ». Nous l'illustrons à travers l'utilisation d'un logiciel d'enseignement assisté par ordinateur. Ce produit réalisé par notre équipe concerne le R.N.I.S. (Réseau Numérique à Intégration de Service). Il permet à un étudiant de se familiariser avec les concepts, les services, l'architecture et la mise en oeuvre d'un réseau R.N.I.S
On stratification control of the velocity fluctuations in sedimentation
International audienceWe have tested whether stratification can govern local velocity fluctuations in suspensions of sedimenting spheres. Comparison of the proposed scaling for local control of fluctuations by stratification to experimental data demonstrates that this mechanism cannot account for the reduction of the observed velocity fluctuations
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