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Communication Dans Un Congrès Année : 2023

Model-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes

Résumé

The disjoint paths logic, FOL+DP, is an extension of First-Order Logic (FOL) with the extra atomic predicate dpk(x1, y1, . . . , xk, yk), expressing the existence of internally vertex-disjoint paths between xi and yi, for i ∈ {1, . . . , k}. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every proper minor-closed graph class, model-checking for FOL+DP can be done in quadratic time. We also introduce an extension of FOL+DP, namely the scattered disjoint paths logic, FOL+SDP, where we further consider the atomic predicate s-sdpk(x1,y1,...,xk,yk), demanding that the disjoint paths are within distance bigger than some fixed value s. Using the same technique we prove that model-checking for FOL+SDP can be done in quadratic time on classes of graphs with bounded Euler genus.
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Dates et versions

hal-04043007 , version 1 (17-10-2023)

Identifiants

Citer

Petr Golovach, Giannos Stamoulis, Dimitrios M. Thilikos. Model-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes. SODA 2023 - ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, Jan 2023, Florence, Italy. pp.3684-3699, ⟨10.1137/1.9781611977554.ch141⟩. ⟨hal-04043007⟩
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