Publications (243)157.56 Total impact
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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 NPcomplete, but polynomialtime solvable for graphs with some special properties. In particular, it is solvable in polynomial time for clawfree 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 polynomialtime algorithm to solve the dominating induced matching problem for graphs containing no long claw.  [Show abstract] [Hide abstract]
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 polynomialtime solvability of the maximum independent set problem.  Discrete Applied Mathematics 07/2014; 171:158. DOI:10.1016/j.dam.2014.01.020 · 0.80 Impact Factor
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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 nonedge 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.  [Show abstract] [Hide abstract]
ABSTRACT: A threedimensional 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 ccedgecolored 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.Discrete Applied Mathematics 04/2014; 182. DOI:10.1016/j.dam.2014.04.010 · 0.80 Impact Factor 
Article: Combinatorial Optimization Preface
Discrete Applied Mathematics 02/2014; 164:11. DOI:10.1016/j.dam.2013.11.011 · 0.80 Impact Factor 

Article: Graph Coloring Problems
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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)]. 
Article: On some coloring problems in grids
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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 NPcomplete case is (2, 3)List coloring with k≥4k≥4 colors. We also show that Precoloring extension with 3 colors is NPcomplete in subgrids.Theoretical Computer Science 02/2013; 472:9–27. DOI:10.1016/j.tcs.2012.10.046 · 0.66 Impact Factor  [Show abstract] [Hide abstract]
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 maximumweight stable sets in G. For any integer d⩾0, a minimum dtransversal 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 polynomialtime algorithm to determine minimum dtransversals in bipartite graphs. Our algorithm is based on a characterization of maximumweight stable sets in bipartite graphs. We also derive results on minimum dtransversals of minimumweight vertex covers in weighted bipartite graphs.Journal of Discrete Algorithms 12/2012; 17:95102. DOI:10.1016/j.jda.2012.06.002  [Show abstract] [Hide abstract]
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.Discrete Mathematics 05/2012; 312(10):18381843. DOI:10.1016/j.disc.2012.01.036 · 0.56 Impact Factor 
Conference Paper: (p,q)  Choosability of Grid Graphs
Annual International Conference on Computational Mathematics, Computational Geometry & Statistics; 01/2012  [Show abstract] [Hide abstract]
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.Progress in Combinatorial Optimization, 11/2011: pages 203222; ISTEWILEY., ISBN: 9781848212060  [Show abstract] [Hide abstract]
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 dtransversal is a subset of V which intersects any optimum solution in at least d elements while a dblocker 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 dtransversals and dblockers of stable sets or vertex covers in bipartite and in split graphs.Journal of Combinatorial Optimization 11/2011; 22(4):857872. DOI:10.1007/s1087801093346 · 0.94 Impact Factor 
Conference Paper: Minimum dTransversals of MaximumWeight Stable Sets in Trees
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ABSTRACT: Given an integer d and a weighted tree T, we show how to find in polynomial time a minimum dtransversal of all maximumweight stable sets in T, i.e., a set of vertices of minimum size having at least d vertices in common with every maximumweight stable set. Our proof relies on new structural results for maximumweight stable sets on trees.European Conference on Combinatorics, Graph Theory and Applications; 10/2011  Annals of Operations Research, Vol. 188 08/2011; Springer.

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ABSTRACT: The splitcoloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring problem from the point of view of splitcoloring, such as criticality and the uniqueness of the minimum splitcoloring. We discuss some properties of splitcritical and uniquely splitcolorable graphs. We describe constructions of such graphs with some additional properties. We also study the effect of the addition and the removal of some edge sets on the value of the splitchromatic number. All these results are compared with their cochromatic counterparts. We conclude with several research directions on the topic.Discrete mathematics & theoretical computer science DMTCS 09/2010; 12(5):124. · 0.32 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this tutorial paper, we consider the basic image reconstruction problem which stems from discrete tomography. We derive a graph theoretical model and we explore some variations and extensions of this model. This allows us to establish connections with scheduling and timetabling applications. The complexity status of these problems is studied and we exhibit some polynomially solvable cases.We show how various classical techniques of operations research like matching, 2SAT, network flows are applied to derive some of these results.Annals of Operations Research 06/2010; 175(1):287307. DOI:10.1007/s1028800800775 · 1.22 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study a multiprocessor extension of the preemptive open shop scheduling problem, where the set of processors is partitioned into processor groups. We show that the makespan minimization problem is polynomially solvable for two multiprocessor groups even if preemptions are restricted to integral times.Operations Research Letters 03/2010; 38(2):129132. DOI:10.1016/j.orl.2009.10.007 · 0.62 Impact Factor
Publication Stats
3k  Citations  
157.56  Total Impact Points  
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Institutions

19732014

École Polytechnique Fédérale de Lausanne
 School of Basic Sciences
Lausanne, Vaud, Switzerland


19742009

Ecole polytechnique fédérale de Lausanne
Lausanne, Vaud, Switzerland


2005

Paris Dauphine University
Lutetia Parisorum, ÎledeFrance, France


2002

École Polytechnique
Paliseau, ÎledeFrance, France


19841996

Eawag: Das WasserforschungsInstitut des ETHBereichs
Duebendorf, Zurich, Switzerland


1988

Beijing Institute Of Technology
Peping, Beijing, China
