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The bidimensional theory of bounded-genus graphs

by Erik D. Demaine, MohammadTaghi Hajiaghayi, Dimitrios M. Thilikos - SIAM JOURNAL ON DISCRETE MATHEMATICS , 2004
"... ..."
Abstract - Cited by 15 (8 self) - Add to MetaCart
Abstract not found

ON THE EXISTENCE OF INFINITELY MANY ESSENTIAL SURFACES OF BOUNDED GENUS

by Ulrich Oertel, A Theorem Of William Jaco, Eric Sedgwick States That
"... 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 - Cited by 5 (0 self) - Add to MetaCart
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

by L. Aleksandrov, H. Djidjev - 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 ..."
Abstract - Cited by 29 (4 self) - Add to MetaCart
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

by Monika Rauch Henzinger, et al. , 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

by Erik D. Demaine, Dimitrios M. Thilikos, et al.
"... ... 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 - Cited by 63 (22 self) - Add to MetaCart
... 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

by Cyril Gavoille, Nicolas Hanusse , 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 - Cited by 31 (12 self) - Add to MetaCart
; 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

by Glencora Borradaile, Erik D. Demaine, Siamak Tazari , 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 ..."
Abstract - Cited by 18 (4 self) - Add to MetaCart
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

by Piotr Indyk, Anastasios Sidiropoulos - PROC. 23RD ANN. ACM SYMP. COMPUT. GEOM , 2007
"... ..."
Abstract - Cited by 17 (5 self) - Add to MetaCart
Abstract not found

Edge Separators For Graphs Of Bounded Genus With Applications

by Ondrej Sykora, Imrich Vrto , 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 ..."
Abstract - Cited by 8 (1 self) - Add to MetaCart
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

by Shayan Oveis Gharan, Amin Saberi
"... 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 ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
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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