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ECCC
2010
143views more  ECCC 2010»
13 years 5 months ago
Space-Efficient Algorithms for Reachability in Surface-Embedded Graphs
We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let G(m, g) be the class of directed acyclic graphs with m = m(n) source ...
Derrick Stolee, N. V. Vinodchandran
JGT
2008
74views more  JGT 2008»
13 years 7 months ago
Straight line embeddings of cubic planar graphs with integer edge lengths
We prove that every simple cubic planar graph admits a planar embedding such that each edge is embedded as a straight line segment of integer length.
Jim Geelen, Anjie Guo, David McKinnon
CORR
2007
Springer
132views Education» more  CORR 2007»
13 years 7 months ago
Nodally 3-connected planar graphs and convex combination mappings
A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a pl...
Colm Ó'Dúnlaing
ESA
2005
Springer
95views Algorithms» more  ESA 2005»
14 years 1 months ago
Finding Shortest Non-separating and Non-contractible Cycles for Topologically Embedded Graphs
We present an algorithm for finding shortest surface non-separating cycles in graphs embedded on surfaces in O(g3/2 V 3/2 log V + g5/2 V 1/2 ) time, where V is the number of vert...
Sergio Cabello, Bojan Mohar
PAMI
2007
154views more  PAMI 2007»
13 years 7 months ago
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction
—Over the past few decades, a large family of algorithms—supervised or unsupervised; stemming from statistics or geometry theory—has been designed to provide different soluti...
Shuicheng Yan, Dong Xu, Benyu Zhang, HongJiang Zha...