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SIAMCOMP
2008
77views more  SIAMCOMP 2008»
14 years 9 months ago
A Linear-Time Approximation Scheme for TSP in Undirected Planar Graphs with Edge-Weights
We give an algorithm requiring O(c1/2 n) time to find an -optimal traveling salesman tour in the shortest-path metric defined by an undirected planar graph with nonnegative edgele...
Philip N. Klein
DCG
2000
84views more  DCG 2000»
14 years 9 months ago
Convex and Linear Orientations of Polytopal Graphs
This paper examines directed graphs related to convex polytopes. For each fixed d-polytope and any acyclic orientation of its graph, we prove there exist both convex and concave fu...
J. Mihalisin, Victor Klee
CORR
2010
Springer
105views Education» more  CORR 2010»
14 years 9 months ago
Exact Shortest Path Queries for Planar Graphs Using Linear Space
We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar gr...
Shay Mozes, Christian Sommer
CCCG
2007
14 years 11 months ago
Straight-line Drawings of Outerplanar Graphs in O(dn log n) Area
We show an algorithm for constructing O(dn log n) area outerplanar straight-line drawings of n-vertex outerplanar graphs with degree d. Also, we settle in the negative a conjectur...
Fabrizio Frati
EJC
2010
14 years 9 months ago
Rank-width and tree-width of H-minor-free graphs
We prove that for any fixed r 2, the tree-width of graphs not containing Kr as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of the...
Fedor V. Fomin, Sang-il Oum, Dimitrios M. Thilikos