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Séminaires du Pôle 2 : "Optimisation combinatoire, algorithmique"

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Fabio Furini et Jerome Monnot

Liste de diffusion.

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florian . sikora @ dauphine . fr

Les séminaires ont lieu en général le lundi à 14h.

Prochains séminaires :

Séminaires précédents :

lundi 11 décembre 2017, 14h, A 304 : Ararat Harutyunyan (LAMSADE) : A disproof of the normal graphs conjecture

Abstract : A graph G is called normal if there exist two coverings, C and S, of its vertex set such that every member of C induces a clique in G, every member of S induces an independent set in G, and any clique in C and independent set in S have a non-empty intersection. Normal graphs derive their motivation from information theory, where they are related to the Shannon capacity of a graph. In particular, they form a family which extends the class of perfect graphs. It was conjectured by De Simone and Körner [DAM ’99] that a graph G is normal if G does not contain C_5, C_7 and the complement of C_7 as an induced subgraph. Using random graphs and rather routine probabilistic methods, we give a disproof of this conjecture.

Joint work with Lucas Pastor (G-SCOP, Grenoble) and Stéphan Thomassé (ENS Lyon).

lundi 20 novembre 2017, 14h, P 301 : Julien Baste (LIP6) : F-M-DELETION parameterized by treewidth

For a fixed collection of graphs F, the F-M-DELETION problem consists in, given a graph G and an integer k, decide whether there exists a set S of vertices of G of size at most k such that G without the vertices of S does not contain any of the graphs of F as a minor. This problem is a generalization of some well known problems as VERTEX COVER (F=K_2), FEEDBACK VERTEX SET (F=K_3), or VERTEX PLANARIZATION (F=K_5, K_3,3 ). We are interested in the parameterized complexity of F-M-DELETION when the parameter is the treewidth of the input graph, denoted by tw. Our objective is to determine, for a fixed F, the smallest function f such that F-M-DELETION can be solved in time f(tw)*poly(n) on n-vertex graphs.

lundi 13 novembre 2017, 14h, salle A (C206, 2ème étage) : Tomáš Toufar (Charles University, Czech Republic) : Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices


We study the Steiner Tree problem, in which a set of terminal vertices
needs to be connected in the cheapest possible way in an edge-weighted
graph. This problem has been extensively studied from the viewpoint of
approximation and also parametrization. In particular, on one hand
Steiner Tree is known to be APX-hard, and W[2]-hard on the other, if
parameterized by the number of non-terminals (Steiner vertices) in the
optimum solution. In contrast to this we
give an efficient parameterized approximation scheme (EPAS), which
circumvents both hardness results. Moreover, our methods imply the
existence of a polynomial size approximate kernelization scheme
(PSAKS) for the assumed parameter.
We further study the parameterized approximability of other variants
of Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For
neither of these an EPAS is likely to exist for the studied parameter :
for Steiner Forest an easy observation shows that the problem is
APX-hard, even if the input graph contains no Steiner vertices. For
Directed Steiner Tree we prove that computing a constant approximation
for this parameter is W[1]-hard. Nevertheless, we
show that an EPAS exists for Unweighted Directed Steiner Tree. Also we
prove that there is an EPAS and a PSAKS for Steiner Forest if in
addition to the number of Steiner vertices, the number of connected
components of an optimal solution is considered to be a parameter.

lundi 16 octobre 2017, 14h, salle A (2ème étage) : Eunjung Kim (LAMSADE) : Erdos-Posa Property of Chordless Cycles and its Applications

A chordless cycle is a cycle of length at least 4 that has no chord. We prove that the class of all chordless cycles has the Erdos-Posa property, which resolves the major open question concerning the Erdos-Posa property. We complement our main result by showing that the class of all chordless cycles of length at least l for any fixed l ≥ 5 does not have the Erdos-Posa property.

Our proof for chordless cycles is constructive : in polynomial time, one can either find k + 1 vertex-disjoint chordless cycles, or ck2 log k vertices hitting every chordless cycle for some constant c. It immediately implies an approximation algorithm of factor O(opt log opt) for Chordal Vertex Deletion, which improves the best known approximation by Agrawal et. al. The improved approximation algorithm entails improvement over the known kernelization for Chordal Vertex Deletion.

As a corollary, for a non-negative integral function w defined on the vertex set of a graph G, the minimum value \sum_x\in S w(x) over all vertex sets S where G − S is forest is at most O(k2 log k) where k is the maximum number of cycles (not necessarily vertex-disjoint) in G such that each vertex v is used at most w(v) times.

lundi 2 octobre 2017, 14h, P303 : Giuseppe F. Italiano (Universita’ di Roma "Tor Vergata") : 2-Connectivity in Directed Graphs

We survey some recent results on 2-edge and 2-vertex
connectivity in directed graphs. Despite being complete analogs of the
corresponding notions on undirected graphs, in digraphs 2-connectivity
has a much richer and more complicated structure. For undirected
graphs it has been known for over 40 years how to compute all bridges,
articulation points, 2-edge- and 2-vertex-connected components in
linear time, by simply using depth first search. In the case of
digraphs, however, the very same problems have been much more
challenging and have been tackled only very recently.

Exposés de 2016-2017.
Exposés de 2015-2016.
Exposés de 2014-2015.

Pour les exposés antérieurs, voir cette page.


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