In the context of distributed certification, the recognition of graph classes
has started to be intensively studied. For instance, different results related
to the recognition of planar, bounded tree-width and H-minor free graphs have
been recently obtained. The goal of the present work is to design compact
certificates for the local recognition of relevant geometric intersection graph
classes, namely interval, chordal, circular arc, trapezoid and permutation.
More precisely, we give proof labeling schemes recognizing each of these
classes with logarithmic-sized certificates. We also provide tight logarithmic
lower bounds on the size of the certificates on the proof labeling schemes for
the recognition of any of the aforementioned geometric intersection graph
classes