Communication Dans Un Congrès Année : 2024

Practical Computation of Graph VC-Dimension

Résumé

For any set system H=(V,R), R2V, a subset SV is called \emph{shattered} if every SS results from the intersection of S with some set in \R. The \emph{VC-dimension} of H is the size of a largest shattered set in V. In this paper, we focus on the problem of computing the VC-dimension of graphs. In particular, given a graph G=(V,E), the VC-dimension of G is defined as the VC-dimension of (V,N), where N contains each subset of V that can be obtained as the closed neighborhood of some vertex vV in G. Our main contribution is an algorithm for computing the VC-dimension of any graph, whose effectiveness is shown through experiments on various types of practical graphs, including graphs with millions of vertices. A key aspect of its efficiency resides in the fact that practical graphs have small VC-dimension, up to 8 in our experiments. As a side-product, we present several new bounds relating the graph VC-dimension to other classical graph theoretical notions. We also establish the W[1]-hardness of the graph VC-dimension problem by extending a previous result for arbitrary set systems.
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hal-04553784 , version 1 (06-05-2024)

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David Coudert, Mónika Csikós, Guillaume Ducoffe, Laurent Viennot. Practical Computation of Graph VC-Dimension. SEA 2024 - Symposium on Experimental Algorithms, Jul 2024, Vienne, Austria. pp.20, ⟨10.4230/LIPIcs.SEA.2024.8⟩. ⟨hal-04553784⟩
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