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We present a logspace algorithm that constructs a canonical intersectionmodel for a given proper circular-arc graph, where `canonical' means thatmodels of isomorphic graphs are equal. This implies that the recognition andthe isomorphism problems for this class of graphs are solvable in logspace. Fora broader class of concave-round graphs, that still possess (not necessarilyproper) circular-arc models, we show that those can also be constructedcanonically in logspace. As a building block for these results, we show how tocompute canonical models of circular-arc hypergraphs in logspace, which arealso known as matrices with the circular-ones property. Finally, we considerthe search version of the Star System Problem that consists in reconstructing agraph from its closed neighborhood hypergraph. We solve it in logspace for theclasses of proper circular-arc, concave-round, and co-convex graphs.

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