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- Uffe Flarup, Pascal Koiran, Laurent Lyaudet
- ISAAC
- 2007

Valiant introduced some 25 years ago an algebraic model of computation along with the complexity classes VP and VNP, which can be viewed as analogues of the classical classes P and NP. They are defined using non-uniform sequences of arithmetic circuits and provides a framework to study the complexity for sequences of polynomials. Prominent examples of… (More)

- Uffe Flarup, Laurent Lyaudet
- Theory of Computing Systems
- 2008

Some 25 years ago Valiant introduced an algebraic model of computation in order to study the complexity of evaluating families of polynomials. The theory was introduced along with the complexity classes VP and VNP which are analogues of the classical classes P and NP. Families of polynomials that are difficult to evaluate (that is, VNP-complete) include the… (More)

- Laurent Lyaudet, Frédéric Mazoit, Stéphan Thomassé
- Eur. J. Comb.
- 2010

In a recent paper, Amini et al. introduced a general framework to prove duality theorems between tree decompositions and their dual combinatorial object. They unify all known ad-hoc proofs in one duality theorem based on submodular partition functions. This general theorem remains however a bit technical and relies on this particular submodularity property.… (More)

- Laurent Lyaudet
- Theor. Comput. Sci.
- 2010

This article presents an infinite family of combinatorial problems that shows abrupt changes of complexity between neighbour problems. We define problem P l k as a purely constraint-driven variant of hypergraph partitioning with parameters k and l as follows: Given a hypergraph on n vertices and k sizes of colours t1, . . . , tk of sum n, can we colour the… (More)

- Laurent Lyaudet
- 2013

The ubiquity of graphs or hypergraphs in algorithmic and in complexity theory is notoriously known since the origin of these problematics. One can cite the numerous data structures using graphs (trees most of the time), flow algorithms, the many optimization problems on graphs that are NP-complete (proper coloring, maximum clique, . . . ), the proof of… (More)

- Laurent Lyaudet, Paulin Melatagia Yonta, Maurice Tchuente, René Ndoundam
- Discrete Math., Alg. and Appl.
- 2013

- Laurent Lyaudet
- 2007

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