Self-adjusting binary search trees
Journal of the ACM (JACM)
A data structure for dynamic trees
Journal of Computer and System Sciences
Offline algorithms for dynamic minimum spanning tree problems
Journal of Algorithms
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Volume Data Mining Using 3D Field Topology Analysis
IEEE Computer Graphics and Applications
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Loops in reeb graphs of 2-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Dynamizing static algorithms, with applications to dynamic trees and history independence
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining information in fully dynamic trees with top trees
ACM Transactions on Algorithms (TALG)
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Harmonic skeleton for realistic character animation
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Reeb spaces of piecewise linear mappings
Proceedings of the twenty-fourth annual symposium on Computational geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Time-varying Reeb graphs for continuous space--time data
Computational Geometry: Theory and Applications
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
Journal of Experimental Algorithmics (JEA)
Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees
IEEE Transactions on Visualization and Computer Graphics
A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
Graph-based representations of point clouds
Graphical Models
An efficient computation of handle and tunnel loops via Reeb graphs
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We present a deterministic algorithm to compute the Reeb graph of a PL real-valued function on a simplicial complex in O(m log m) time, where m is the size of the 2-skeleton. The problem reduces to dynamic graph connectivity. We obtain the running time by using offline graph connectivity which assumes that the sequence of operations is known in advance. The algorithm is implemented and experimental results are given. In addition, we reduce the offline graph connectivity problem to computing the Reeb graph.