202 research outputs found
The 0-1 inverse maximum stable set problem
Given an instance of a weighted combinatorial optimization problem and its feasible solution, the usual inverse problem is to modify as little as possible (with respect to a fixed norm) the given weight system to make the giiven feasible solution optimal. We focus on its 0-1 version, which is to modify as little as possible the structure of the given instance so that the fixed solution becomes optimal in the new instance. In this paper, we consider the 0-1 inverse maximum stable set problem against a specific (optimal or not) algorithm, which is to delete as few vertices as possible so that the fixed stable set S* can be returned as a solution by the given algorithm in the new instance. Firstly, we study the hardness and approximation results of the 0-1 inverse maximum stable set problem against the algorithms. Greedy and 2-opt. Secondly, we identify classes of graphs for which the 0-1 inverse maximum stable set problem can be polynomially solvable. We prove the tractability of the problem for several classes of perfect graphs such as comparability graphs and chordal graphs.Combinatorial inverse optimization, maximum stable set problem, NP-hardness, performance ratio, perfect graphs.
On-line bin-packing problem : maximizing the number of unused bins
In this paper, we study the on-line version of the bin-packing problem. We analyze the approximation behavior of an on-line bin-packing algorithm under an approximation criterion called differential ratio. We are interested in two types of results : the differential competitivity ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problem and for the quality of the algorithm developed to solve it. In its off-line version, the bin-packing problem, BP, is better approximated in differential framework than in standard one. Our objective is to determine if or not such result exists for the on-line version of BP.On-line algorithm, bin-packing problem, competitivity ratio.
Structure of conflict graphs in constraint alignment problems and algorithms
We consider the constrained graph alignment problem which has applications in
biological network analysis. Given two input graphs , a pair of vertex mappings induces an {\it edge conservation} if
the vertex pairs are adjacent in their respective graphs. %In general terms The
goal is to provide a one-to-one mapping between the vertices of the input
graphs in order to maximize edge conservation. However the allowed mappings are
restricted since each vertex from (resp. ) is allowed to be mapped
to at most (resp. ) specified vertices in (resp. ). Most
of results in this paper deal with the case which attracted most
attention in the related literature. We formulate the problem as a maximum
independent set problem in a related {\em conflict graph} and investigate
structural properties of this graph in terms of forbidden subgraphs. We are
interested, in particular, in excluding certain wheals, fans, cliques or claws
(all terms are defined in the paper), which corresponds in excluding certain
cycles, paths, cliques or independent sets in the neighborhood of each vertex.
Then, we investigate algorithmic consequences of some of these properties,
which illustrates the potential of this approach and raises new horizons for
further works. In particular this approach allows us to reinterpret a known
polynomial case in terms of conflict graph and to improve known approximation
and fixed-parameter tractability results through efficiently solving the
maximum independent set problem in conflict graphs. Some of our new
approximation results involve approximation ratios that are function of the
optimal value, in particular its square root; this kind of results cannot be
achieved for maximum independent set in general graphs.Comment: 22 pages, 6 figure
Playing with parameters: structural parameterization in graphs
When considering a graph problem from a parameterized point of view, the
parameter chosen is often the size of an optimal solution of this problem (the
"standard" parameter). A natural subject for investigation is what happens when
we parameterize such a problem by various other parameters, some of which may
be the values of optimal solutions to different problems. Such research is
known as parameterized ecology. In this paper, we investigate seven natural
vertex problems, along with their respective parameters: the size of a maximum
independent set, the size of a minimum vertex cover, the size of a maximum
clique, the chromatic number, the size of a minimum dominating set, the size of
a minimum independent dominating set and the size of a minimum feedback vertex
set. We study the parameterized complexity of each of these problems with
respect to the standard parameter of the others.Comment: 17 page
On-line vertex-covering
AbstractWe study the minimum vertex-covering problem under two on-line models corresponding to two different ways vertices are revealed. The former one implies that the input-graph is revealed vertex-by-vertex. The second model implies that the input-graph is revealed per clusters, i.e. per induced subgraphs of the final graph. Under the cluster-model, we then relax the constraint that the choice of the part of the final solution dealing with each cluster has to be irrevocable, by allowing backtracking. We assume that one can change decisions upon a vertex membership of the final solution, this change implying, however, some cost depending on the number of the vertices changed
Differential approximation results for the Steiner tree problem
International audienceWe study the approximability of three versions of the Steiner tree problem. For the first one where the input graph is only supposed connected, we show that it is not approximable within better than |V \setminus N|^{-r} for any r in [0,1], where V and N are the vertex-set of the input graph and the set of terminal vertices, respectively. For the second of the Steiner tree versions considered, the one where the input graph is supposed complete and the edge distances are arbitrary, we prove that it can be differentially approximated within 1/2. For the third one defined on complete graphs with edge distances 1 or 2, we show that it is differentially approximable within 0.82. Also, we extend the result of (M. Bern and P. Plassmann, The Steiner problem with edge lengths 1 and 2, Inform. Process. Lett. 32, 1989), we show that the Steiner tree problem with edge lengths 1 and 2 is MaxSNP-complete even in the case where |V| 0. This allows us to finally show that Steiner tree problem with edge lengths 1 and 2 cannot by approximated by polynomial time differential approximation schemata
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