Solving the Canonical Representation and Star System Problems for Proper Circular-Arc Graphs in Logspace

We present a logspace algorithm that constructs a canonical intersection model for a given proper circular-arc graph, where canonical means that models of isomorphic graphs are equal. This implies that the recognition and the isomorphism problems for this class of graphs are solvable in logspace. For a broader class of concave-round graphs, that still possess (not necessary proper) circular-arc models, we show that the latter can also be constructed canonically in logspace. Finally, we consider the search version of the Star System Problem that consists in reconstruction of a graph from its closed neighborhood hypergraph. We solve it in logspace for the classes of proper circular-arc, concave-round, and co-convex graphs.