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890
On the upward planarity of mixed plane graphs
, 2014
"... A mixed plane graph is a plane graph whose edge set is partitioned into a set of directed edges and a set of undirected edges. An orientation of a mixed plane graph G is an assignment of directions to the undirected edges of G resulting in a directed plane graph ~G. In this paper, we study the compu ..."
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the computational complexity of testing whether a given mixed plane graph G is upward planar, i.e., whether it can be oriented to obtain a directed plane graph ~G such that ~G admits a planar drawing in which each edge is represented by a ymonotone curve. Our contribution is threefold. First, we show that upward
Routing with Guaranteed Delivery in ad hoc Wireless Networks
, 2001
"... We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication of ..."
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Cited by 849 (80 self)
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We consider routing problems in ad hoc wireless networks modeled as unit graphs in which nodes are points in the plane and two nodes can communicate if the distance between them is less than some fixed unit. We describe the first distributed algorithms for routing that do not require duplication
An Approach for Mixed Upward Planarization
 In Proc. 7th International Workshop on Algorithms and Data Structures (WADS’01
, 2003
"... In this paper, we consider the problem of finding a mixed upward planarization of a mixed graph, i.e., a graph with directed and undirected edges. The problem is a generalization of the planarization problem for undirected graphs and is motivated by several applications in graph drawing. ..."
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Cited by 17 (2 self)
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In this paper, we consider the problem of finding a mixed upward planarization of a mixed graph, i.e., a graph with directed and undirected edges. The problem is a generalization of the planarization problem for undirected graphs and is motivated by several applications in graph drawing.
Upward Planar Graphs and their Duals
, 2015
"... We consider upward planar drawings of directed graphs in the plane (UP), and on standing (SUP) and rolling cylinders (RUP). In the plane and on the standing cylinder the edge curves are monotonically increasing in ydirection. On the rolling cylinder they wind unidirectionally around the cylinder. T ..."
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We consider upward planar drawings of directed graphs in the plane (UP), and on standing (SUP) and rolling cylinders (RUP). In the plane and on the standing cylinder the edge curves are monotonically increasing in ydirection. On the rolling cylinder they wind unidirectionally around the cylinder
Efficient planarity testing
 J. ASSOC. COMPUT. MACH
, 1974
"... This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm uses depthfirst sear ..."
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Cited by 278 (5 self)
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This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm uses depth
The Duals of Upward Planar Graphs on Cylinders
"... We consider directed planar graphs with an upward planar drawing on the rolling and standing cylinders. These classes extend the upward planar graphs in the plane. Here, we address the dual graphs. Our main result is a combinatorial characterization of these sets of upward planar graphs. It basical ..."
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Cited by 2 (2 self)
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We consider directed planar graphs with an upward planar drawing on the rolling and standing cylinders. These classes extend the upward planar graphs in the plane. Here, we address the dual graphs. Our main result is a combinatorial characterization of these sets of upward planar graphs
Upward and quasiupward planarity testing of embedded mixed graphs
, 2012
"... Mixed graphs have both directed and undirected edges and received considerable attention in the literature. We study two upward planarity testing problems for embedded mixed graphs, give some complexity results, and describe Integer Linear Programming techniques to solve them. Experiments show the e ..."
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Cited by 1 (0 self)
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Mixed graphs have both directed and undirected edges and received considerable attention in the literature. We study two upward planarity testing problems for embedded mixed graphs, give some complexity results, and describe Integer Linear Programming techniques to solve them. Experiments show
Classification of Planar Upward Embedding
"... We consider planar upward drawings of directed graphs on arbitrary surfaces where the upward direction is defined by a vector field. This generalizes earlier approaches using surfaces with a fixed embedding in R 3 and introduces new classes of planar upward drawable graphs, where some of them even ..."
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Cited by 3 (3 self)
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homogeneous field on a cylinder and with a radial field in the plane. A cyclic field in the plane introduces the new class RUP of upward drawable graphs, which can be embedded on a rolling cylinder. We establish strict inclusions for planar upward drawability on the plane, the sphere, the rolling cylinder
On the Computational Complexity of Upward and Rectilinear Planarity Testing (Extended Abstract)
, 1994
"... A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical se ..."
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Cited by 106 (4 self)
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A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical
Rolling Upward Planarity Testing of Strongly Connected Graphs
"... A graph is upward planar if it can be drawn without edge crossings such that all edges point upward. Upward planar graphs have been studied on the plane, the standing and rolling cylinders. For all these surfaces, the respective decision problem N Phard in general. Efficient algorithms exist if the ..."
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Cited by 1 (1 self)
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A graph is upward planar if it can be drawn without edge crossings such that all edges point upward. Upward planar graphs have been studied on the plane, the standing and rolling cylinders. For all these surfaces, the respective decision problem N Phard in general. Efficient algorithms exist
Results 1  10
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