Decidability of string graphs

Authors:
Marcus Schaefer;Daniel Stefankovic
Affiliations:
Department of Computer Science, DePaul University, 243 South Wabash, Chicago, Illinois;Department of Computer Science, University of Chicago, 1100 East 58th Street, Chicago, Illinois and Department of Computer Science, Comenius University, Bratislava, Slovakia
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

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Abstract

We show that string graphs can be recognized in nondeterministic exponential time by giving an exponential upper bound on the number of intersections for a drawing realizing the string graph in the plane. This upper bound confirms a conjecture by Kratochv\'{\i}l and Matou\v{s}ek~\cite{KM91} and settles the long-standing open problem of the decidability of string graph recognition (Sinden~\cite{S66}, Graham~\cite{G76}). Finally we show how to apply the result to solve another old open problem: deciding the existence of Euler diagrams, a central problem of topological inference (Grigni, Papadias, Papadimitriou~\cite{GPP95}).