Circular Ones Matrices and the Stable Set Polytope of Quasi-Line Graphs
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Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...
Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in correlated Erdös-Rény ...
An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n.Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed p ...
This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly construc ...
In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...
EPFL2019
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 Ctr2016
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Graphs are now ubiquitous in almost every field of research. Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged. Focusing on dynamical processes, we propose a fast, robust and scalable framewor ...
Haxell's condition [14] is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the existence of a perf ...
SPRINGER HEIDELBERG2018
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We present an efficient matching method for generalized geometric graphs. Such graphs consist of vertices in space connected by curves and can represent many real world structures such as road networks in remote sensing, or vessel networks in medical imagi ...
