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Map Graphs
, 1999
"... We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, and an O(n³)time ..."
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Cited by 37 (3 self)
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We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give an NP characterization for such graphs, and an O(n³)time recognition algorithm for a restricted version: given a graph, decide whether it is realized by adjacencies in a map without holes, in which at most four nations meet at any point.
Upward Planar Drawing of Single Source Acyclic Digraphs
, 1990
"... A upward plane drawing of a directed acyclic graph is a straight line drawing in the Euclidean plane such that all directed arcs point upwards. Thomassen [30] has given a nonalgorithmic, graphtheoretic characterization of those directed graphs with a single source that admit an upward drawing. We ..."
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Cited by 17 (0 self)
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A upward plane drawing of a directed acyclic graph is a straight line drawing in the Euclidean plane such that all directed arcs point upwards. Thomassen [30] has given a nonalgorithmic, graphtheoretic characterization of those directed graphs with a single source that admit an upward drawing. We present an efficient algorithm to test whether a given singlesource acyclic digraph has a plane upward drawing and, if so, to find a representation of one such drawing. The algorithm decomposes the graph into biconnected and triconnected components, and defines conditions for merging the components into an upward drawing of the original graph. For the triconnected components we provide a linear algorithm to test whether a given plane representation admits an upward drawing with the same faces and outer face, which also gives a simpler (and algorithmic) proof of Thomassen's result. The entire testing algorithm (for general single source directed acyclic graphs) operates in O(n²) time and...
FADE: A Layout Facility for Graphbased Diagrams
, 1994
"... In this paper we present a novel approach to the layout problem of 2dimensional graphbased diagrams. We introduce a framework for efficiently solving constrained layout problems encompassing geometrical and graphbased algorithms especially dedicated to the generation of diagrams. These concepts a ..."
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In this paper we present a novel approach to the layout problem of 2dimensional graphbased diagrams. We introduce a framework for efficiently solving constrained layout problems encompassing geometrical and graphbased algorithms especially dedicated to the generation of diagrams. These concepts as well as the aesthetics for the readability of diagrams are presented by introducing FADE 1 . FADE is a userparametrizable framework for the generation of EXPRESSG diagrams. Our present implementation is discussed considering extensions to other classes of graphs and layout problems. Additionally, competitive approaches in this domain and their limitations are critically reviewed. 1 Introduction Interactive visual modeling plays an important role in science. Therefore, there is an increasing interest in pictorial representations since they can more concisely capture relevant information rather than a pure text document. In many cases, the information can be modeled by a graph or a hy...