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» Planar graph bipartization in linear time
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ESA
2009
Springer
127views Algorithms» more  ESA 2009»
14 years 26 days ago
Maximum Flow in Directed Planar Graphs with Vertex Capacities
In this paper we present an O(n log n) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the...
Haim Kaplan, Yahav Nussbaum
CORR
2010
Springer
105views Education» more  CORR 2010»
13 years 6 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
WADS
2007
Springer
165views Algorithms» more  WADS 2007»
14 years 11 days ago
A Near Linear Time Approximation Scheme for Steiner Tree Among Obstacles in the Plane
We present a polynomial-time approximation scheme (PTAS) for the Steiner tree problem with polygonal obstacles in the plane with running time O(n log2 n), where n denotes the numb...
Matthias Müller-Hannemann, Siamak Tazari
LATIN
2010
Springer
14 years 1 months ago
Optimal Polygonal Representation of Planar Graphs
In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of pl...
Emden R. Gansner, Yifan Hu, Michael Kaufmann, Step...
ALGORITHMICA
2006
132views more  ALGORITHMICA 2006»
13 years 6 months ago
Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs
Hierarchical graphs and clustered graphs are useful non-classical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clus...
Peter Eades, Qing-Wen Feng, Xuemin Lin, Hiroshi Na...