The one-dimensional Euclidean domain: Finitely many obstructions are not enough

Gerhard J. Woeginger; Jiehua Chen; Kirk Pruhs

The one-dimensional Euclidean domain: Finitely many obstructions are not enough

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arxiv 1506.03838 v1 pith:5NQXOPJ4 submitted 2015-06-11 cs.GT

Jiehua Chen , Kirk Pruhs , Gerhard J. Woeginger This is my paper · ORCID

classification cs.GT

keywords euclideanfinitelymanyone-dimensionalpreferenceprofilesbeencase

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We show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.

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A suite of convex-hull forbidden substructures, reduction rules, ILP, and QCP recognizes 2-Euclidean elections quickly, solving 283 more PrefLib instances than the previous algorithm.

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