The computational complexity of knot and link problems
Journal of the ACM (JACM)
Transforming curves on surfaces
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Recognizing string graphs in NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
3-manifold knot genus is NP-complete
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Efficient Algorithms for Lempel-Zip Encoding (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Solvability of Equations in Free Partially Commutative Groups Is Decidable
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Application of Lempel-Ziv Encodings to the Solution of Words Equations
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Algorithms on Compressed Strings and Arrays
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Tracing compressed curves in triangulated surfaces
Proceedings of the twenty-eighth annual symposium on Computational geometry
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We derive several algorithms for curves and surfaces represented using normal coordinates. The normal coordinate representation is a very succinct representation of curves and surfaces. For embedded curves, for example, its size is logarithmically smaller than a representation by edge intersections in a triangulation. Consequently, fast algorithms for normal representations can be exponentially faster than algorithms working on the edge intersection representation. Normal representations have been essential in establishing bounds on the complexity of recognizing the unknot [Hak61, HLP99, AHT02], and string graphs [SS驴02]. In this paper we present efficient algorithms for counting the number of connected components of curves and surfaces, deciding whether two curves are isotopic, and computing the algebraic intersection numbers of two curves. Our main tool are equations over monoids, also known as word equations.