# Cyril GavoilleUniversity of Bordeaux · LaBRI (UMR 5800)

Cyril Gavoille

## About

232

Publications

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## Publications

Publications (232)

We consider q-coloured words, that is words on \(\left\{ {{1},\dots ,{q}}\right\} \) where no two consecutive letters are equal. Motivated by multipartite colouring games with nonsignalling resources, we are interested in random q-coloured words satisfying a k-localisability property. More precisely, the probability of containing any given pair of...

A partition . (C1,C2,...,Cq) of . G=(V,E) into clusters of strong (respectively, weak) diameter . d, such that the supergraph obtained by contracting each . Ci is . ℓ-colorable is called a strong (resp., weak) . (d,ℓ)-network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Aw...

Let $S$ be a finite set of points in the plane that are in convex position. We present an algorithm that constructs a plane $\frac{3+4\pi}{3}$-spanner of $S$ whose vertex degree is at most 3. Let $\Lambda$ be the vertex set of a finite non-uniform rectangular lattice in the plane. We present an algorithm that constructs a plane $3\sqrt{2}$-spanner...

This article proposes a forbidden-set labeling scheme for the family of unweighted graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ϵ > 0, the labeling scheme stores an O(1 + ϵ-1)2α log2 n-bit label at each vertex. Given the labels of two end-vertices s and t, and the label...

This book constitutes the proceedings of the 30th International Symposium on Distributed Computing, DISC 2016, held in Paris, France, in September 2016.
The 32 full papers, 10 brief annoucements and 3 invited lectures presented in this volume were carefully reviewed and selected from 145 submissions.The focus of the conference is on following topic...

This paper investigates compact routing schemes that are very efficient with respect to the memory used to store routing tables in internet-like graphs. We propose a new compact name-independent routing scheme whose theoretically proven average memory per node is upper-bounded by n γ , with constant γ < 1/2, while the maximum memory of any node is...

This paper investigates compact routing schemes that are very efficient with respect to the memory used to store routing tables in internet-like graphs. We propose a new compact name-independent routing scheme whose theoretically proven average memory per node is upper-bounded by nγ, with constant γ

Cet article étudie les schémas de routage compacts qui sont très efficaces en termes de mémoires utilisées pour le stockage des tables de routage dans les graphes de type Internet. Nous proposons un nouveau schéma de routage compact avec indépendance des noms, dont la mémoire moyenne par noeud est prouvée comme étant bornée par √n, et pour lequel l...

Cet article étudie les schémas de routage compacts qui sont très efficaces en termes de mémoires utilisées pour le stockage des tables de routage dans les graphes de type Internet. Nous proposons un nouveau schéma de routage compact avec indépendance des noms, dont la mémoire moyenne par noeud est prouvée comme étant bornée par √n, et pour lequel l...

A partition $(C_1,C_2,...,C_q)$ of $G = (V,E)$ into clusters of strong
(respectively, weak) diameter $d$, such that the supergraph obtained by
contracting each $C_i$ is $\ell$-colorable is called a strong (resp., weak)
$(d, \ell)$-network-decomposition. Network-decompositions were introduced in a
seminal paper by Awerbuch, Goldberg, Luby and Plotki...

We consider how to assign labels to any undirected graph with n nodes such
that, given the labels of two nodes and no other information regarding the
graph, it is possible to determine the distance between the two nodes. The
challenge in such a distance labeling scheme is primarily to minimize the
maximum label lenght and secondarily to minimize th...

In this paper we determine the exact stretch factor of L∞L∞-Delaunay triangulations of points in the plane. We do this not only when the distance between the points is defined by the usual L2L2-metric but also when it is defined by the LpLp-metric, for any p∈[1,∞]p∈[1,∞]. We then apply this result to compute the exact stretch factor of L1L1-Delauna...

We prove that any graph excluding $K_r$ as a minor has can be partitioned
into clusters of diameter at most $\Delta$ while removing at most $O(r/\Delta)$
fraction of the edges. This improves over the results of Fakcharoenphol and
Talwar, who building on the work of Klein, Plotkin and Rao gave a partitioning
that required to remove $O(r^2/\Delta)$ f...

We present a distributed asynchronous algorithm that, for every undirected weighted n-node graph G, constructs name-independent routing tables for G. The size of each table is \(\tilde{O}(\sqrt{n}\,)\), whereas the length of any route is stretched by a factor of at most 7 w.r.t. the shortest path. At any step, the memory space of each node is \(\ti...

In this paper we determine the stretch factor of L
1-Delaunay and L
∞ -Delaunay triangulations, and we show that it is equal to \(\sqrt{4+2\sqrt{2}} \approx 2.61\). Between any two points x,y of such triangulations, we construct a path whose length is no more than \(\sqrt{4+2\sqrt{2}}\) times the Euclidean distance between x and y, and this bound i...

This paper considers fully dynamic (1+ε) distance oracles and (1+ε) forbidden-set labeling schemes for planar graphs. For a given n-vertex planar graph G with edge weights drawn from [1,M] and parameter ε>0, our forbidden-set labeling scheme uses labels of length λ = O(ε⁻¹ log²n log(nM) • maxlogn). Given the labels of two vertices s and t and of a...

In this paper we determine the stretch factor of the $L_1$-Delaunay and
$L_\infty$-Delaunay triangulations, and we show that this stretch is
$\sqrt{4+2\sqrt{2}} \approx 2.61$. Between any two points $x,y$ of such
triangulations, we construct a path whose length is no more than
$\sqrt{4+2\sqrt{2}}$ times the Euclidean distance between $x$ and $y$, a...

Motivated by multipath routing, we introduce a multi-connected variant of spanners. For that purpose we introduce the p-multipath cost between two nodes u and v as the minimum weight of a collection of p internally vertex-disjoint paths between u and v. Given a weighted graph G, a subgraph H is a p-multipath s-spanner if for all u,v, the p-multipat...

For every integral parameter k > 1, given an unweighted graph G, we construct in polynomial time, for each vertex u, a distance label L(u) of size \({\tilde{O}}(n^{2/(2k-1)})\). For any u,v ∈ G, given L(u),L(v) we can return in time O(k) an affine approximation \(\hat{d}(u,v)\) on the distance d(u,v) between u and v in G such that \(d(u,v) \leqslan...

Routing with multiplicative stretch 3 (which means that the path used by the routing scheme can be up to three times longer than a shortest path) can be done with routing tables of Θ(√n) bits per node. The space lower bound is due to the existence of dense graphs with large girth. Dense graphs can be sparsified to subgraphs, called spanners, with v...

Fraigniaud et al., (2001) and independently Thorup et al., (2001) show that n-node trees support routing schemes with message headers, node addresses, and routing tables of O(log n) bits. It still open to known if this optimal result can be extended to the tree-width two graphs. The best known routing scheme require O(log2 n) bits (cf. (Peleg, 2000...

Rapport de contrat (final)

We provide the first sparse covers and probabilistic partitions for graphs excluding a fixed minor that have strong diameter bounds; i.e. each set of the cover/partition has a small diameter as an induced sub-graph. Using these results we provide improved distributed name-independent routing schemes. Specifically, given a graph excluding a minor on...

In this paper we investigate the structural properties of k-path separable graphs, that are the graphs that can be separated by a set of k shortest paths. We identify several graph families having such path separability, and we show that this property is closed
under minor taking. In particular we establish a list of forbidden minors for 1-path sep...

We consider the question: “What is the smallest degree that can be achieved for a plane spanner of a Euclidean graph E\mathcal E?” The best known bound on the degree is 14. We show that E\mathcal E always contains a plane spanner of maximum degree6 and stretch factor6. This spanner can be constructed efficiently in
linear time given the Triangular...

The paper proposes a forbidden-set labeling scheme for the family of graphs with doubling dimension bounded by fi. For an n-vertex graph G in this family, and for any desired precision parameter † > 0, the labeling scheme stores an O(1+† ¡1 ) 2fi log 2 n-bit label at each vertex. Given the labels of two end-vertices s and t, and the labels of a set...

Θk
-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to a factor depending on the cone number k and the dimension of the space.
TD-Delaunay graphs, a.k.a. triangular-distance Delaunay triangulations, introduced by Chew, have b...

This paper concerns graph spanners that approximate multipaths between pair of vertices of an undirected graphs with n vertices. Classically, a spanner H of stretch s for a graph G is a spanning subgraph such that the distance in H between any two vertices is at most s times the distance in G. We study in this paper spanners that approximate short...

The so called \emph{quantum game theory} has recently been proclaimed as one of the new branches in the development of both quantum information theory and game theory. However, the notion of a quantum game itself has never been strictly defined, which has led to a lot of conceptual confusion among different authors. In this paper we introduce a new...

Cet article concerne des graphes de recouvrement (ci-après nommés {em spanneurs}) qui approximent des multichemins entre des paires de sommets de graphes non orientés de $n$ sommets. Habituellement un spanneur $H$ d'étirement $s$ pour un graphe $G$ est un sous-graphe couvrant tel que la distance dans $H$ entre deux sommets quelconques est au plus $...

Cet article concerne les graphes de recouvrement d'un ensemble fini de points du plan Euclidien. Un graphe de recouvrement $H$ est de facteur d'étirement $t$ pour un ensemble de points $S$ si, entre deux points quelconques de $S$, le coût d'un plus court chemin dans $H$ est au plus $t$ fois leur distance Euclidenne. Les graphes de recouvrement d'ét...

An (α,β)-spanner of a graph G is a subgraph H that approximates distances in G within a multiplicative factor α and an additive error β, ensuring that for any two nodes u,v, d
H
(u,v) ≤ α·d
G
(u,v) + β. This paper concerns algorithms for the distributed deterministic construction of a sparse (α,β)-spanner H for a given graph G and distortion para...

It is known that every weighted planar graph with n vertices contains three shortest paths whose removal halves the graph into connected components of at most n/2 vertices. Whether this property remains true with the use of two shortest paths only is an open problem. We show that two shortest paths are enough for a large family of planar graphs, ca...

We prove that every planar graph G of tree-length ℓ has a tree-decomposition for which every bag is the union of at most 10 shortest paths of length O(ℓ)O(ℓ). As a consequence, the tree-width of G is bounded by O(ℓ)O(ℓ), generalizing the linear local tree-width result of planar graphs, since the tree-length of a graph does not exceed its diameter....

Distributed Greedy Coloring is an interesting and intuitive variation of the standard Coloring problem. Given an order among the colors, a coloring is said to be "greedy" if there does not exist a vertex for which its associated color can be replaced by a color of lower position in the fixed order without violating the property that neighbouring ve...

Augmented graphs were introduced for the purpose of analyzing the “six degrees of separation between individuals” observed experimentally by the sociologist Standley Milgram in the 60’s. We define an augmented graph as a pair (G,M) where G is an n-node graph with nodes labeled in {1,…,n}, and M is an n×n stochastic matrix. Every node u∈V(G) is give...

Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed computation is extended so as to apply quantum processing. This has been achieved in one of two distinct ways: (1) by i...

We study the problem of the amount of information (advice) about a graph that must be given to its nodes in order to achieve fast distributed computations. The required size of the advice enables to measure the information sensitivity of a network problem. A problem is information sensitive if little advice is enough to solve the problem rapidly (i...

Un spanner est un sous-graphe $H$ couvrant les sommets d'un graphe $G$ et qui approxime les distances de $G$. L'étirement de $H$ est borné par une fonction $s$, on parle alors de $s$-spanner, si $d_H(u,v) \le s(d_G(u,v))$ pour tous sommets $u,v$ de $G$. De nombreux travaux concernent l'étude du compromis entre la taille du spanner (\cad son nombre...

We consider the problem of determining in a planar graph G whether two vertices x and y are linked by a path that avoids a set X of vertices and a set F of edges. We attach labels to vertices in such a way that this fact can be determined from the labels of x and y, the vertices in X and the ends of the edges of F. For a planar graph with n vertice...

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices.
We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of every
class that is nicely locally clique-width-decomposable. This notion generalizes that of a nicely l...

We define a vertex labelling for every planar 3-connected graph with n vertices from which one can answer connectivity queries. A connectivity query asks whether there exists in the given graph a path linking u and v that avoids a set F of edges and a set X of vertices. The vertices u,v and those of X are given by their labels. The edges of F are g...

A distance labeling scheme is a distributed graph representation that assigns labels to the vertices and enables answering distance queries between any pair (x, y) of vertices by using only the labels of x and y. This paper presents an optimal distance labeling scheme with labels of O(log n) bits for the n-vertex interval graphs family. It improves...

This paper concerns the efficient construction of sparse and low stretch spanners for unweighted arbitrary graphs with n nodes. All previous deterministic distributed algorithms, for constant stretch spanners of o(n2) edges, have a running time Ω(nϵ) for some constant ϵ>0 depending on the stretch. Our deterministic distributed algorithms construct...

We prove that there exists an O(log(n))-labeling scheme for every first-order formula with free set variables in every class of graphs that is nicely locally cwd-decomposable , which contains in particular, the nicely locally tree- decomposable classes. For every class of bounded expansionwe prove that every bounded formulahas an O(log(n))-labeling...

Graph augmentation theory is a general framework for ana- lyzing navigability in social networks. It is known that, for large classes of graphs, there exist augmentations of these graphs such that greedy routing according to the shortest path metric performs in polylogarithmic expected number of steps. However, it is also known that there are class...

The paper presents a deterministic distributed algorithm that, given k 1, constructs in k rounds a (2k−1, 0)-spanner of O(kn1+1/k )e dges for everyn-node unweighted graph. (If n is not available to the nodes, then our algorithm executes in 3k − 2 rounds, and still returns a (2k − 1, 0)-spanner with O(kn1+1/k) edges.) Previous distributed solutions...

International audience
In this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of edges), that is 4kn + 2n + o(...

We consider a distributed representation scheme for trees, supporting some special relationships between nodes at small distance. For instance, we show that for a tree T and an integer k we can assign local information on nodes such that we can decide for any two nodes u and v if the distance between u and v is at most k and if so, compute it only...

Implicit representation of graphs is a coding of the structure of graphs using distinct labels so that adjacency between any two vertices can be decided by inspecting their labels alone. All previous implicit representations of planar graphs were based on the classical three forests decomposition technique (a.k.a. Schnyder’s trees), yielding asympt...