Dominique de Werra

École Polytechnique Fédérale de Lausanne, Lausanne, Vaud, Switzerland

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Publications (249)160.78 Total impact

  • Marc Demange · Dominique de Werra
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    ABSTRACT: A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs when the number $k$ of colors is limited. We get results which differ surprisingly from the usual case where $k$ is implicit and which extend known results for the usual case. We also exhibit some classes of graphs (defined by structural properties of their blocks) which are choosable. Finally we show that for any $\ell\geq 3$ and any $k\geq 2\ell-2$ there is a bipartite graph which is $\ell$-choosable with $k$ colors but not with $k+1$.
    No preview · Article · Jan 2016
  • M.-C. Costa · D. de Werra · C. Picouleau
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    ABSTRACT: Given a positive integer n we find a graph G=(V,E) on |V|=n vertices with a minimum number of edges such that for any pair of non adjacent vertices x,y the graph G-x-y contains a (almost) perfect matching M. Intuitively the non edge xy and M form a (almost) perfect matching of G. Similarly we determine a graph G=(V,E) with a minimum number of edges such that for any matching M¯ of the complement G¯ of G with size ⌊n2⌋-1, G-V(M¯) contains an edge e. Here M¯ and the edge e of G form a (almost) perfect matching of G¯.We characterize these minimal graphs for all values of n.
    No preview · Article · Dec 2015
  • Alain Hertz · Vadim Lozin · Bernard Ries · Victor Zamaraev · Dominique de Werra
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    ABSTRACT: An induced matching $M$ in a graph $G$ is dominating if every edge not in $M$ shares exactly one vertex with an edge in $M$. The dominating induced matching problem (also known as efficient edge domination) asks whether a graph $G$ contains a dominating induced matching. This problem is generally NP-complete, but polynomial-time solvable for graphs with some special properties. In particular, it is solvable in polynomial time for claw-free graphs. In the present paper, we study this problem for graphs containing no long claw, i.e. no induced subgraph obtained from the claw by subdividing each of its edges exactly once. To solve the problem in this class, we reduce it to the following question: given a graph $G$ and a subset of its vertices, does $G$ contain a matching saturating all vertices of the subset? We show that this question can be answered in polynomial time, thus providing a polynomial-time algorithm to solve the dominating induced matching problem for graphs containing no long claw.
    No preview · Article · May 2015
  • D. de Werra · A. Hertz
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    ABSTRACT: Variations and extensions of the basic vertex-colouring and edge-colouring models have been developed to deal with increasingly complex scheduling problems. We present and illustrate them in specific situations where additional requirements are imposed. We include list-colouring, mixed graph colouring, co-colouring, colouring with preferences and bandwidth colouring, and we present applications of edge-colourings to open shop, school timetabling and sports scheduling problems. We also discuss balancing and compactness constraints which often appear in practical situations. Introduction We show here how graph colouring models may provide a natural tool for dealing with a variety of scheduling problems. Starting from the basic vertex-colouring model, we will introduce some variations and extensions that are motivated by their applications to some scheduling issues. In each case we give references for further results and for extensions of the various models presented. For algorithms, see Chapter 13. In chromatic scheduling problems we have a collection V of items, such as operations of jobs to be performed. In V there are some pairs v, w that are subject to an incompatibility condition and we call E the set of such incompatibility pairs. These data are represented by the graph G = (V, E) in which the items are associated with the vertices and the incompatible pairs v, w with the edges vw between the corresponding vertices. We also have a set C = {1, 2, …, k} of time periods (of unit duration). Assuming that each item (considered as an operation) has unit completion time, we may ask whether we can find a schedule taking the incompatibilities into account and using at most k periods of time. This is precisely the vertex k-colouring problem: there exists a feasible schedule if and only if the set V of vertices can be partitioned into subsets S1, S2, …, Sk, where each Si contains no two incompatible items. In some instances, we may try to find the smallest set C of periods (that is, the smallest k) for which a schedule in time k = |C| exists.
    No preview · Chapter · Jan 2015
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    Konrad K. Dabrowski · Dominique de Werra · Vadim V. Lozin · Viktor Zamaraev
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    ABSTRACT: The notion of augmenting graphs generalizes Berge's idea of augmenting chains, which was used by Edmonds in his celebrated solution of the maximum matching problem. This problem is a special case of the more general maximum independent set (MIS) problem. Recently, the augmenting graph approach has been successfully applied to solve MIS in various other special cases. However, our knowledge of augmenting graphs is still very limited, and we do not even know what the minimal infinite classes of augmenting graphs are. In the present paper, we find an answer to this question and apply it to extend the area of polynomial-time solvability of the maximum independent set problem.
    Preview · Article · Oct 2014 · Graphs and Combinatorics
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    T. Ekim · N.V.R. Mahadev · D. de Werra

    Preview · Article · Jul 2014 · Discrete Applied Mathematics
  • Christophe Picouleau · Dominique de Werra · Marie-Christine Costa
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    ABSTRACT: We define as extensible a graph G such that for every pair u,v of non adjacent vertices it is possible to extend the non-edge uv to a perfect (or near perfect) matching using only edges of G that are not incident to u or v. For every order n of G we give Ext(n) the minimum size of an extensible graph.
    No preview · Article · Apr 2014
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    ABSTRACT: A three-dimensional Nuclear Magnetic Resonance (NMR) map displays the results of NMR experiments, that allow to determine the shape of a biological molecule. Shape calculation starts from a reconstruction of a sequence of NMR signals, which is equivalent to finding a specific path in a graph representation of the problem. Let G=(V,E)G=(V,E) be a graph that models the interactions reflected on an NMR map. Its edges are colored with cc colors, where each color corresponds to one of cc different relationships between the signals. The sequence of interactions under consideration is represented using a concept of an orderly colored path in the cc-edge-colored graph. In this paper, we consider the problem of finding the required arrangement of NMR signals on the 3D map and we present its graph representation. We discuss the computational complexity of the problem, we consider its two alternative integer programming models, and evaluate the performance of an optimization algorithm based on the solution of their relaxation combined with the separation of fractional cycles in a Branch & Cut scheme.
    Full-text · Article · Apr 2014 · Discrete Applied Mathematics
  • Dominique de Werra · Nelson Maculan · A. Ridha Mahjoub

    No preview · Article · Feb 2014 · Discrete Applied Mathematics
  • T. Ekim · N. V. R. Mahadev · D. De Werra

    No preview · Article · Jan 2014
  • Dominique de Werra · Daniel Kobler
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    ABSTRACT: We present the basic concepts of colorings as well as a series of variations and generalizations prompted by various scheduling problems including drawing up school timetables. A few recent exact algorithms and some heuristics will be presented. In particular we will give an outline of methods based on the tabu search for finding approximate solutions for large problems. Lastly, we mention application of colorings to various problems, including computer file transfers and production systems. This text is an extended version of [D. de Werra and D. Kobler, RAIRO, Oper. Res. 37, No. 1, 29–66 (2003; Zbl 1062.90026)].
    No preview · Article · Feb 2013
  • Marc Demange · Dominique De Werra
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    ABSTRACT: We study complexity issues related to some coloring problems in grids: we examine in particular the case of List coloring, of Precoloring extension and of (p,q)(p,q)-List coloring, the case of List coloring in bipartite graphs where lists in the first part of the bipartition are all of size pp and lists in the second part are of size qq. In particular, we characterize the complexity of (p,q)(p,q)-List coloring in grid graphs, showing that the only NP-complete case is (2, 3)-List coloring with k≥4k≥4 colors. We also show that Precoloring extension with 3 colors is NP-complete in subgrids.
    No preview · Article · Feb 2013 · Theoretical Computer Science
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    ABSTRACT: Let G=(V,E) be a graph in which every vertex v∈V has a weight w(v)⩾0 and a cost c(v)⩾0. Let SG be the family of all maximum-weight stable sets in G. For any integer d⩾0, a minimum d-transversal in the graph G with respect to SG is a subset of vertices T⊆V of minimum total cost such that |T∩S|⩾d for every S∈SG. In this paper, we present a polynomial-time algorithm to determine minimum d-transversals in bipartite graphs. Our algorithm is based on a characterization of maximum-weight stable sets in bipartite graphs. We also derive results on minimum d-transversals of minimum-weight vertex covers in weighted bipartite graphs.
    No preview · Article · Dec 2012 · Journal of Discrete Algorithms
  • Bernard Ries · Dominique de Werra · Rico Zenklusen
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    ABSTRACT: In threshold graphs one may find weights for the vertices and a threshold value t such that for any subset S of vertices, the sum of the weights is at most the threshold t if and only if the set S is a stable (independent) set. In this note we ask a similar question about vertex colorings: given an integer p, when is it possible to find weights (in general depending on p) for the vertices and a threshold value tp such that for any subset S of vertices the sum of the weights is at most tp if and only if S generates a subgraph with chromatic number at most p−1? We show that threshold graphs do have this property and we show that one can even find weights which are valid for all values of p simultaneously.
    No preview · Article · May 2012 · Discrete Mathematics
  • Marc Demange · Dominique De Werra

    No preview · Conference Paper · Jan 2012
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    ABSTRACT: A general formulation of the problems we are going to consider may be sketched as follows: we are given a system S which is operated by an actor A; this actor tries to choose among several optimal actions which may be represented by subsets of S. An opponent O wants to prevent actor A from operating S in an optimum way by destroying some part P of S. O may in particular wish to find a part P of S as small as possible whose removal will reduce the efficiency of the operation of the system S by a given amount. Another way for O would be to determine a smallest possible part P (the most vital elements) which hits in a sufficient amount every possible optimal action of A. This kind of problem occurs in various situation related to safety or reliability or even in game theoretic contexts. Such problems have been studied from a theoretical point of view in very special cases for which combinatorial optimization models may give an acceptable represen- tation of S. It leads to challenging optimization problems; the goal of this chapter is to give a partial survey of such situations while focusing on simple models based on graphs and other (hopefully tractable) combinatorial structures.
    No preview · Chapter · Nov 2011
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    Marie-Christine Costa · Dominique de Werra · Christophe Picouleau
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    ABSTRACT: We consider a set V of elements and an optimization problem on V: the search for a maximum (or minimum) cardinality subset of V verifying a given property ℘. A d-transversal is a subset of V which intersects any optimum solution in at least d elements while a d-blocker is a subset of V whose removal deteriorates the value of an optimum solution by at least d. We present some general characteristics of these problems, we review some situations which have been studied (matchings, s–t paths and s–t cuts in graphs) and we study d-transversals and d-blockers of stable sets or vertex covers in bipartite and in split graphs.
    Preview · Article · Nov 2011 · Journal of Combinatorial Optimization
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    ABSTRACT: Given an integer d and a weighted tree T, we show how to find in polynomial time a minimum d-transversal of all maximum-weight stable sets in T, i.e., a set of vertices of minimum size having at least d vertices in common with every maximum-weight stable set. Our proof relies on new structural results for maximum-weight stable sets on trees.
    No preview · Conference Paper · Oct 2011
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    Endre Boros · Yves Crama · Dominique de Werra · Pierre Hansen · Frédéric Maffray

    Full-text · Book · Aug 2011
  • Endre Boros · Yves Crama · Dominique de Werra · Pierre Hansen · Frédéric Maffray

    No preview · Article · Jan 2011

Publication Stats

4k Citations
160.78 Total Impact Points

Institutions

  • 1973-2014
    • École Polytechnique Fédérale de Lausanne
      • School of Basic Sciences
      Lausanne, Vaud, Switzerland
  • 2002
    • École Polytechnique
      Paliseau, Île-de-France, France
  • 1984-1996
    • Eawag: Das Wasserforschungs-Institut des ETH-Bereichs
      Duebendorf, Zurich, Switzerland
    • Poznan University of Technology
      Posen, Greater Poland Voivodeship, Poland
  • 1988
    • Beijing Institute Of Technology
      Peping, Beijing, China
  • 1974
    • Ecole polytechnique fédérale de Lausanne
      Lausanne, Vaud, Switzerland