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Publications associées (159)
Extension complexity of stable set polytopes of bipartite graphs
Yuri Faenza, Manuel Francesco Aprile
The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...
Springer2017Diverse M-Best Solutions by Dynamic Programming
Michaël Unser, Virginie Sophie Uhlmann
Many computer vision pipelines involve dynamic programming primitives such as finding a shortest path or the minimum energy solution in a tree-shaped probabilistic graphical model. In such cases, extracting not merely the best, but the set of M-best soluti ...
Springer2017A semi-algebraic version of Zarankiewicz's problem
A bipartite graph G is semi-algebraic in R-d if its vertices are represented by point sets P,Q subset of R-d and its edges are defined as pairs of points (p,q) epsilon P x Q that satisfy a Boolean combination of a fixed number of polynomial equations and i ...
European Mathematical Soc2017Spinner: Scalable Graph Partitioning in the Cloud
Andreas Loukas, Dionysios Logothetis
In this paper, we present a graph partitioning algorithm to partition graphs with trillions of edges. To achieve such scale, our solution leverages the vertex-centric Pregel abstraction provided by Giraph, a system for large-scale graph analytics. We desig ...
Ieee2017Independence number of generalized Petersen graphs
Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed towa ...
Charles Babbage Res Ctr2016Scaling a Reliable Distributed System
Alexandre David Olivier Maurer
We consider the problem of reliably connecting an arbitrarily large set of computers (nodes) with communication channels. Reliability means here the ability, for any two nodes, to remain connected (i.e., their ability to communicate) with probability at le ...
LPD EPFL2016Simple topological graphs
This thesis is devoted to the understanding of topological graphs. We consider the following four problems: 1. A \emph{simple topological graph} is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any t ...
EPFL2016On the Zarankiewicz problem for intersection hypergraphs
Let d and t be fixed positive integers, and let denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem ...
Academic Press Inc Elsevier Science2016Decomposition of Multiple Packings with Subquadratic Union Complexity
János Pach, Bartosz Maria Walczak
Suppose k is a positive integer and X is a k-fold packing of the plane by infinitely many arc-connected compact sets, which means that every point of the plane belongs to at most k sets. Suppose there is a function f(n) = o(n(2)) with the property that any ...
Cambridge Univ Press2016A Precise Threshold For Quasi-Ramsey Numbers
We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...
Siam Publications2015