Topological graph theory
A data structure for dynamic trees
Journal of Computer and System Sciences
Computational complexity of combinatorial surfaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Maintenance of a minimum spanning forest in a dynamic plane graph
Journal of Algorithms
Approximation algorithms for NP-complete problems on planar graphs
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Separator based sparsification I.: planarity testing and minimum spanning trees
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Linear Algorithms for Partitioning Embedded Graphs of BoundedGenus
SIAM Journal on Discrete Mathematics
Disk packings and planar separators
Proceedings of the twelfth annual symposium on Computational geometry
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Optimally cutting a surface into a disk
Proceedings of the eighteenth annual symposium on Computational geometry
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
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
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Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Finding shortest contractible and shortest separating cycles in embedded graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
Homology flows, cohomology cuts
Proceedings of the forty-first annual ACM symposium on Theory of computing
Finding shortest contractible and shortest separating cycles in embedded graphs
ACM Transactions on Algorithms (TALG)
Output-sensitive algorithm for the edge-width of an embedded graph
Proceedings of the twenty-sixth annual symposium on Computational geometry
Finding shortest non-trivial cycles in directed graphs on surfaces
Proceedings of the twenty-sixth annual symposium on Computational geometry
ACM Transactions on Algorithms (TALG)
Maximum flows and parametric shortest paths in planar graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shortest cut graph of a surface with prescribed vertex set
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Algorithms and theory of computation handbook
Shortest non-trivial cycles in directed surface graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Tightening Nonsimple Paths and Cycles on Surfaces
SIAM Journal on Computing
Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Shortest non-crossing walks in the plane
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Algorithms for the edge-width of an embedded graph
Computational Geometry: Theory and Applications
Fully dynamic approximate distance oracles for planar graphs via forbidden-set distance labels
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Testing graph isotopies on surfaces
Proceedings of the twenty-eighth annual symposium on Computational geometry
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
Controlled-distortion constrained global parametrization
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Structured recursive separator decompositions for planar graphs in linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Digital geometry processing with discrete exterior calculus
ACM SIGGRAPH 2013 Courses
Dynamic programming for graphs on surfaces
ACM Transactions on Algorithms (TALG)
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We provide a data structure for maintaining an embedding of a graph on a surface (represented combinatorially by a permutation of edges around each vertex) and computing generators of the fundamental group of the surface, in amortized time O(log n + log g(log log g)3) per update on a surface of genus g; we can also test orientability of the surface in the same time, and maintain the minimum and maximum spanning tree of the graph in time O(log n + log4 g) per update. Our data structure allows edge insertion and deletion as well as the dual operations; these operations may implicitly change the genus of the embedding surface. We apply similar ideas to improve the constant factor in a separator theorem for low-genus graphs, and to find in linear time a tree-decomposition of low-genus low-diameter graphs.