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Structures arborescentes : problèmes algorithmiques et combinatoires

Abstract : The first part is devoted to enumerative combinatorics. In the third first chapters, we study the families of Cayley trees such that the root is lower than its sons under some combinatorial parameters (number of vertices, label of the root, inversion polynomial), and of alternating trees. Most of our proofs are based on bijections. In the next chapter, we are interested in the enumeration of colored trees, with the formula of Good-Lagrange (inversion of multivariated formal power series). We give a new bijective proof of a variant of this formula and apply this proof in the enumeration and random generation of arborescent structures (like planar cacti). We conclude this part by a proof of a (new) formula for the enumeration of constellation under the number of vertices and faces. In the second part, we study the problem of tree pattern matching, using a classical data structure (for words): the suffix tree. We propose a new tree pattern matching algorithm, based on encoding a tree with words and using the suffix tree of one of these words, which seems to have good experimental properties. We conclude by proposing a notion of suffix tree of a tree and an algorithme computing such a structure.
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https://tel.archives-ouvertes.fr/tel-00007388
Contributor : Cedric Chauve <>
Submitted on : Friday, November 12, 2004 - 11:26:47 PM
Last modification on : Tuesday, October 30, 2018 - 3:04:00 PM
Long-term archiving on: : Thursday, September 13, 2012 - 12:50:31 PM

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  • HAL Id : tel-00007388, version 1

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Cedric Chauve. Structures arborescentes : problèmes algorithmiques et combinatoires. Autre [cs.OH]. Université Sciences et Technologies - Bordeaux I, 2000. Français. ⟨tel-00007388⟩

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