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Tree-Representation of Set Families in Graph Decompositions and Efficient Algorithms

Binh-Minh Bui-Xuan 1
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We address some issues around three main topics: on the representation of set families by a tree, on decompositions of graphs, and on algorithms on graphs.
Our study ranges from theoretical questions in combinatorics to the design of algorithms in computational biology, and also includes several decomposition schemes of graphs, as well as some issues in combinatorial optimization.

The first half of the thesis has two foci.
Firstly, in order to estimate the number of set families satisfying some closure axioms, we have developed new tools and techniques to find tree-like representations for them. Then, we have given some applications of the previous results in a branch of graph theory called graph decomposition.

The second half of the thesis is devoted to algorithmic applications of set representations and decompositions to three graph problems.
For each of them we show how the philosophy of decomposition can help to provide efficient solutions.
We also show how to apply our three solutions to solve three other graph problems.
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Submitted on : Wednesday, November 19, 2008 - 10:50:20 PM
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Binh-Minh Bui-Xuan. Tree-Representation of Set Families in Graph Decompositions and Efficient Algorithms. Computer Science [cs]. Université Montpellier II - Sciences et Techniques du Languedoc, 2008. English. ⟨tel-00340109⟩

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