https://cnrs.hal.science/hal-03727579Araújo, PauloPauloAraújoUFC - Universidade Federal do Ceará = Federal University of CearáCampêlo, ManoelManoelCampêloUFC - Universidade Federal do Ceará = Federal University of CearáCorrêa, RicardoRicardoCorrêaFederal Rural University of Rio de JaneiroLabbé, MartineMartineLabbéInteger Programming Models and Polyhedral Study for the Geodesic Classification Problem on GraphsHAL CCSD2022classificationgeodesic convexitypolyhedral combinatorics[INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO]Labbé, Martine2022-07-19 13:42:512022-07-21 10:06:292022-07-21 10:06:29enPreprints, Working Papers, ...application/pdf1We study a discrete version of the classical classification problem in the Euclidean space, to be called geodesic classification problem. It is defined on a graph, where some vertices are initially assigned a class and the remaining ones must be classified. This vertex partition into classes is grounded on the concept of geodesic convexity on graphs, as a replacement for the Euclidean convexity in the multidimensional space. We propose two new integer programming models along with branch-and-cut algorithms to solve them. We also carry out a polyhedral study of the associated polyhedra, which includes families of facet-defining inequalities and separation algorithms. Finally, we run computational experiments to evaluate the computational efficiency and the classification accuracy of the proposed approaches by comparing them with classic solution methods for the Euclidean convexity classification problem.