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» Connecting face hitting sets in planar graphs
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DIALM
2005
ACM
100views Algorithms» more  DIALM 2005»
13 years 7 months ago
On the pitfalls of geographic face routing
Geographic face routing algorithms have been widely studied in the literature [1, 8, 13]. All face routing algorithms rely on two primitives: planarization and face traversal. The...
Young-Jin Kim, Ramesh Govindan, Brad Karp, Scott S...
JGAA
2006
108views more  JGAA 2006»
13 years 5 months ago
Planar embeddability of the vertices of a graph using a fixed point set is NP-hard
Let G = (V, E) be a graph with n vertices and let P be a set of n points in the plane. We show that deciding whether there is a planar straight-line embedding of G such that the v...
Sergio Cabello
ISAAC
2003
Springer
96views Algorithms» more  ISAAC 2003»
13 years 10 months ago
On the Geometric Dilation of Finite Point Sets
Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclid...
Annette Ebbers-Baumann, Ansgar Grüne, Rolf Kl...
DM
2002
97views more  DM 2002»
13 years 5 months ago
Resonance graphs of catacondensed even ring systems are median
Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R(G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric differenc...
Sandi Klavzar, Petra Zigert, Gunnar Brinkmann
ICALP
2007
Springer
13 years 11 months ago
Linear Problem Kernels for NP-Hard Problems on Planar Graphs
Abstract. We develop a generic framework for deriving linear-size problem kernels for NP-hard problems on planar graphs. We demonstrate the usefulness of our framework in several c...
Jiong Guo, Rolf Niedermeier