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- Chandra Chekuri, Guyslain Naves, F. Bruce Shepherd
- ICALP
- 2013

We consider the approximability of the maximum edge-disjoint paths problem (MEDP) in undirected graphs, and in particular, the integrality gap of the natural multicommodity flow based relaxation for it. The integrality gap is known to be Ω( √ n) even for planar graphs [14] due to a simple topological obstruction and a major focus, following earlier work… (More)

- Guyslain Naves, András Sebö
- Bonn Workshop of Combinatorial Optimization
- 2008

The Directed Steiner Tree (DST) problem is a cornerstone problem in network design. We focus on the generalization of the problem with higher connectivity requirements. The problem with one root and two sinks is APX-hard. The problem with one root and many sinks is as hard to approximate as the directed Steiner forest problem, and the latter is well known… (More)

- Jérémie Chalopin, Victor Chepoi, Guyslain Naves
- Discrete & Computational Geometry
- 2015

In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into L1. As a corollary, we obtain that all planar graphs which are 1skeletons of planar non-positively curved complexes with regular Euclidean polygons as cells are L1-embeddable with distortion at most 2 + π/2 < 4. Our results… (More)

- Guyslain Naves, Nicolas Sonnerat, Adrian Vetta
- APPROX-RANDOM
- 2010

We consider the question: What is the maximum flow achievable in a network if the flow must be decomposable into a collection of edgedisjoint paths? Equivalently, we wish to find a maximum weighted packing of disjoint paths, where the weight of a path is the minimum capacity of an edge on the path. Our main result is an Ω(log n) lower bound on the… (More)

- Guyslain Naves
- Math. Program.
- 2012

We prove the NP-completeness of the integer multiflow problem in planar graphs, with the following restrictions: there are only two demand edges, both lying on the infinite face of the routing graph. This was one of the open challenges concerning disjoint paths, explicitly asked by Müller [5]. It also strengthens Schwärzler’s recent proof of one of the open… (More)

- Guyslain Naves, Vincent Jost
- ArXiv
- 2011

We are given a graph G, an independant set S ⊂ V (G) of terminals, and a function w : V (G) → N. We want to know if the maximum w-packing of vertex-disjoint paths with extremities in S is equal to the minimum weight of a vertex-cut separating S. We call Mader-Mengerian the graphs with this property for each independant set S and each weight function w. We… (More)

- Guyslain Naves, Arnaud Spiwack
- ITP
- 2014

Starting with an algorithm to turn lists into full trees which uses non-obvious invariants and partial functions, we progressively encode the invariants in the types of the data, removing most of the burden of a correctness proof. The invariants are encoded using non-uniform inductive types which parallel numerical representations in a style advertised by… (More)

- Guyslain Naves
- ArXiv
- 2010

We give an algorithm with complexity O(f(R) 2 kn) for the integer multiflow problem on instances (G,H, r, c) with G an acyclic planar digraph and r + c Eulerian. Here, f is a polynomial function, n = |V (G)|, k = |E(H)| and R is the maximum request maxh∈E(H) r(h). When k is fixed, this gives a polynomial algorithm for the arc-disjoint paths problem under… (More)

- Joanne Close, Guyslain Naves
- Annales de la nutrition et de l'alimentation
- 1958