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Results 1 - 10
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981
The bidimensional theory of bounded-genus graphs
- SIAM JOURNAL ON DISCRETE MATHEMATICS
, 2004
"... ..."
ON THE EXISTENCE OF INFINITELY MANY ESSENTIAL SURFACES OF BOUNDED GENUS
"... if M is an irreducible, ∂-irreducible 3-manifold with boundary a single torus, and if M contains no genus one essential (incompressible and ∂-incompressible) surfaces, then M cannot contain infinitely many distinct isotopy classes of essential surfaces of uniformly bounded genus. The main result in ..."
Abstract
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Cited by 5 (0 self)
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if M is an irreducible, ∂-irreducible 3-manifold with boundary a single torus, and if M contains no genus one essential (incompressible and ∂-incompressible) surfaces, then M cannot contain infinitely many distinct isotopy classes of essential surfaces of uniformly bounded genus. The main result
Linear Algorithms for Partitioning Embedded Graphs of Bounded Genus
- SIAM Journal of Discrete Mathematics
, 1996
"... This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus. For any arbitrarily small positive " we show that any n-vertex graph G of genus g can be divided in O(n + g) time into components whose sizes do not exceed "n by removing a set ..."
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Cited by 29 (4 self)
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This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus. For any arbitrarily small positive " we show that any n-vertex graph G of genus g can be divided in O(n + g) time into components whose sizes do not exceed "n by removing a
Fully dynamic algorithms for bounded genus graphs
, 1997
"... We present a deterministic algorithm that maintains the connected components of a graph as edges are inserted and deleted, provided the genus of the graph is bounded by a fixed constant. The algorithm runs in O(log2 n) amortized time per insertion, O(log3 n) amortized time per deletion, and O(log n ..."
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We present a deterministic algorithm that maintains the connected components of a graph as edges are inserted and deleted, provided the genus of the graph is bounded by a fixed constant. The algorithm runs in O(log2 n) amortized time per insertion, O(log3 n) amortized time per deletion, and O
Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free Graphs
"... ... Building on these results, we develop subexponential fixed-parameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, bounded-genus graphs, single-crossing ..."
Abstract
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Cited by 63 (22 self)
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... Building on these results, we develop subexponential fixed-parameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph H as a minor. Inparticular, this general category of graphs includes planar graphs, bounded-genus graphs, single
Compact Routing Tables for Graphs of Bounded Genus
, 2000
"... This paper deals with compact shortest path routing tables on weighted graphs with n nodes. For planar graphs we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log 2+ n) bit-operations per node to extract the route, for any constant > ..."
Abstract
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Cited by 31 (12 self)
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; 0. We obtain the same bounds for graphs of crossing-edge number bounded by o(n= log n), and we generalize for graphs of genus bounded by > 0 yielding a size of n log +O(n) bits per node. Actually we prove a sharp upper bound of 2n log k +O(n) for graphs of pagenumber k, and a lower bound of n log
Polynomial-time approximation schemes for subset-connectivity problems in bounded-genus graphs
, 2009
"... We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both orien ..."
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Cited by 18 (4 self)
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We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both
Probabilistic embeddings of bounded genus graphs into planar graphs
- PROC. 23RD ANN. ACM SYMP. COMPUT. GEOM
, 2007
"... ..."
Edge Separators For Graphs Of Bounded Genus With Applications
, 1993
"... We prove that every n-vertex graph of genus g and maximal degree k has an edge separator of size O( gkn). The upper bound is best possible to within a constant factor. This extends known results on planar graphs and similar results about vertex separators. We apply the edge separator to the is ..."
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Cited by 8 (1 self)
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We prove that every n-vertex graph of genus g and maximal degree k has an edge separator of size O( gkn). The upper bound is best possible to within a constant factor. This extends known results on planar graphs and similar results about vertex separators. We apply the edge separator
The Asymmetric Traveling Salesman Problem on Graphs with Bounded Genus
"... We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the Held-Karp linear programming relaxation has bounded orientable genus. 1 ..."
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Cited by 5 (0 self)
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We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the Held-Karp linear programming relaxation has bounded orientable genus. 1
Results 1 - 10
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981
