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Data structures and network algorithms
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SIAM Journal on Computing
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Network flows: theory, algorithms, and applications
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Efficient computation of geodesic shortest paths
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Computing a canonical polygonal schema of an orientable triangulated surface
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IEEE Transactions on Visualization and Computer Graphics
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal System of Loops on an Orientable Surface
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Spectral partitioning, eigenvalue bounds, and circle packings for graphs of bounded genus
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Conformal virtual colon flattening
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Computing surface hyperbolic structure and real projective structure
Proceedings of the 2006 ACM symposium on Solid and physical modeling
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
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
Optimal pants decompositions and shortest homotopic cycles on an orientable surface
Journal of the ACM (JACM)
Computing general geometric structures on surfaces using Ricci flow
Computer-Aided Design
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Cycle bases of graphs and sampled manifolds
Computer Aided Geometric Design
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Geodesic Delaunay triangulation and witness complex in the plane
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Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Surface matching using consistent pants decomposition
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Splitting (complicated) surfaces is hard
Computational Geometry: Theory and Applications
Testing contractibility in planar rips complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Chain homotopies for object topological representations
Discrete Applied Mathematics
Computing Fundamental Group of General 3-Manifold
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Cut locus and topology from surface point data
Proceedings of the twenty-fifth annual symposium on Computational geometry
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
Measuring and computing natural generators for homology groups
Computational Geometry: Theory and Applications
Computing handle and tunnel loops with knot linking
Computer-Aided Design
C∞ smooth freeform surfaces over hyperbolic domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Finding shortest contractible and shortest separating cycles in embedded graphs
ACM Transactions on Algorithms (TALG)
Optimal homologous cycles, total unimodularity, and linear programming
Proceedings of the forty-second ACM symposium on Theory of computing
Output-sensitive algorithm for the edge-width of an embedded graph
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Finding shortest non-trivial cycles in directed graphs on surfaces
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Approximating loops in a shortest homology basis from point data
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ACM Transactions on Algorithms (TALG)
Genus and the geometry of the cut graph
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Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shortest cut graph of a surface with prescribed vertex set
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Algorithms and theory of computation handbook
Determining edge expansion and other connectivity measures of graphs of bounded genus
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Shape analysis of vestibular systems in adolescent idiopathic scoliosis using geodesic spectra
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The tight orthogonal homotopic bases of closed oriented triangulated surfaces and their computing
Computers & Mathematics with Applications
Improved algorithms for min cut and max flow in undirected planar graphs
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Shortest non-trivial cycles in directed surface graphs
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Euclidean geodesic loops on high-genus surfaces applied to the morphometry of vestibular systems
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Automatic construction of statistical shape models for vertebrae
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Computer-Aided Design
Computing shortest words via shortest loops on hyperbolic surfaces
Computer-Aided Design
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SIAM Journal on Computing
Optimal Homologous Cycles, Total Unimodularity, and Linear Programming
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Global minimum cuts in surface embedded graphs
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Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
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Algorithms for the edge-width of an embedded graph
Computational Geometry: Theory and Applications
Reusing integer homology information of binary digital images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Automatic generation of riemann surface meshes
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Global parametrization by incremental flattening
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Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
Testing graph isotopies on surfaces
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A fast algorithm to compute cohomology group generators of orientable 2-manifolds
Pattern Recognition Letters
Finding Cycles with Topological Properties in Embedded Graphs
SIAM Journal on Discrete Mathematics
Topological detection on wormholes in wireless ad hoc and sensor networks
IEEE/ACM Transactions on Networking (TON)
Annotating simplices with a homology basis and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Efficient topological cleaning for visual colon surface flattening
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Digital geometry processing with discrete exterior calculus
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We describe simple greedy algorithms to construct the shortest set of loops that generates either the fundamental group (with a given basepoint) or the first homology group (over any fixed coefficient field) of any oriented 2-manifold. In particular, we show that the shortest set of loops that generate the fundamental group of any oriented combinatorial 2-manifold, with any given basepoint, can be constructed in O(n log n) time using a straightforward application of Dijkstra's shortest path algorithm. This solves an open problem of Colin de Verdière and Lazarus.