Embeddings of graphs with no short noncontractible cycles
Journal of Combinatorial Theory Series B
Quasi-optimal upper bounds for simplex range searching and new zone theorems
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Transforming curves on surfaces
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Communications of the ACM
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Computing homotopic shortest paths in the plane
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
On Spanning Trees with Low Crossing Numbers
Data Structures and Efficient Algorithms, Final Report on the DFG Special Joint Initiative
GRIN'01 No description on Graphics interface 2001
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Discrete & Computational Geometry
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Many distances in planar graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Splitting (complicated) surfaces is hard
Proceedings of the twenty-second annual symposium on Computational geometry
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Coverage and hole-detection in sensor networks via homology
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
Computing homotopic shortest paths efficiently
Computational Geometry: Theory and Applications
Finding Shortest Non-Separating and Non-Contractible Cycles for Topologically Embedded Graphs
Discrete & Computational Geometry
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Multiple source shortest paths in a genus g graph
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms via contraction decomposition
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Asymptotic stability of switched higher order laplacians
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Cut locus and topology from surface point data
Proceedings of the twenty-fifth annual symposium on Computational geometry
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The (Vietoris-)Rips complex of a discrete point-set P is an abstract simplicial complex in which a subset of P defines a simplex if and only if the diameter of that subset is at most 1. We describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Our algorithm requires O(m log n) time to preprocess a set of n points in the plane in which m pairs have distance at most 1; after preprocessing, deciding whether a cycle of k Rips edges is contractible requires O(k) time. We also describe an algorithm to compute the shortest non-contractible cycle in a planar Rips complex in O(n2log n + mn) time.