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Graph Drawing � Graph Drawing Pro ceedings of the ALCOM International Workshop on Graph Drawing Sevres Parc of Saint Cloud Paris Septemb er Edited by G Di Battista P Eades H de Fraysseix P Rosenstiehl and R Tamassia DRAFT do not distribute Septemb er ALCOM International Workshop on Graph Drawing Sevres Parc of Saint Cloud Paris Septemb er Graph drawing addresses the problem of constructing geometric representations of abstract graphs and networks It is an emerging area of research that combines avors of graph theory and computational geometry The automatic generation of drawings of graphs has imp ortant applications in key computer technologies such as software enginering database design and visual interfaces Further challenging applications can b e found in architectural design circuit schematics and pro ject management Research on graph drawing has b een esp ecially active in the last decade Recent progress in computational geometry top ological graph theory and order theory has considerably aected the evolution of this eld and has widened the range of issues b eing investigated This rst international workshop on graph drawing covers ma jor trends in the area Pap ers describ e theorems algorithms graph drawing systems mathematical and exp erimental analyses practical exp erience and a wide variety of op en problems Authors come from diverse academic cultures from graph theory computational geometry and software engineering Supp ort from ALCOM I I ESPRIT BA and by EHESS is gratefully acknowledged we would also like to thank Mr David Montgomery for preparing this do cument Giusepp e Di Battista Univ Rome Italy dibattistaiasirmcnrit Peter Eades Univ Newcastle Australia eadescsnewcastleeduau Hub ert de Fraysseix CNRS France prosenstdmiensfr Pierre Rosenstiehl EHESS France prosenstdmiensfr Rob erto Tamassia Brown Univ USA rtcsbrownedu Contents J Pach New Developments in Geometric Graph Theory Prosenjit Bose William Lenhart and Giusepp e Liotta Characterizing Proximity Trees Franz J Brandenburg and Peter Eades A Note on a Separator Algorithm for Tree Embeddings and its Application to Free Tree Drawings Brian Regan Two Algorithms for Drawing Trees in Three Dimensions Go os Kant Giusepp e Liotta Rob erto Tamassia and Ioannis G Tollis Area Require ment of Visibility Representations of Trees Ashim Garg and Rob erto Tamassia Ecient Computation of Planar StraightLine Upward Drawings Uli Fomeier and Michael Kaufmann An Approach for BendMinimal Upward Drawing CThomassen Representations of Planar Graphs Patrice Ossona de Mendez On Lattice Structures Induced by Orientations Jan Krato chvl and Jir Matousek Complexity of Intersection Classes of Graphs Hub ert de Fraysseix Patrice Ossona de Mendez and Pierre Rosenstiehl On Triangle Contact Graphs Simone Pimont and Michel Terrenoire Characterisation and Construction of the Rect angular Dual of a Graph Go os Kant and Xin He Two Algorithms for Finding Rectangular Duals of Planar Graphs Go os Kant A More Compact Visibility Representation Anna Lubiw Cone Visibility Graphs Bo jan Mohar Circle Packing Representations in Polynomial Time Bo jan Mohar Martin Juvan and Joze Marincek Obstructions for Embedding Extension Problems Antoine Bergey Automorphisms and Genus on Generalised Maps Ivan Rival Upward Drawing on Surfaces Bo jan Mohar and Pierre Rosenstiehl Tessalation and Visibility Representations of Maps on the Torus Teresa M Przytycka and Jozef H Przytycki A Simple Construction of High Repre sentativity Triangulations Prosenjit Bose Hazel Everett Sandor Fekete Anna Lubiw Henk Meijer Kathleen Romanik Tom Shermer and Sue Whitesides On a Visibility Representation for Graphs in Three Dimensions Jianer Chen Saro ja P Kanchi and Jonathan L Gross On Graph Drawings with Smal lest Number of Faces Marc Bousset A Flow Model of Low Complexity for Twisting a Layout Giusepp e Di Battista Giusepp e Liotta and Francesco Vargiu Convex and nonConvex Cost Functions of Orthogonal Representations Giusepp e Di Battista and Luca Vismara Topology and Geometry of Planar Triangular Graphs Frank Dehne Hristo Djidjev and JorgRudiger Sack An Optimal PRAM Algorithms for Planar Convex Embedding Miki Shimabara Miyauchi Algorithms for Embedding Graphs Into a page Book Hossam ElGindy Michael Houle Bill Lenhart Mirka Miller David Rappap ort and Sue Whitesides Dominance Drawings of Bipartite Graphs Ulrich Finke and Klaus Hinrichs Computing the Overlay of Regular Planar Subdivi sions in Linear Time Alain Denise Generation of Random Planar Maps Joseph Manning Symmetric Drawings of Graphs Tomaz Pisanski Recognizing Symmetric Graphs Peter Eades and Tao Lin Algorithmic and Declarative Approaches to Aesthetic Layout Isab el F Cruz Rob erto Tamassia and Pascal Van Hentenryck A Visual Approach to Graph Drawing Gaby Zinmeister Layout of Trees with Attribute Graph Grammars Sandra P Foubister and Colin Runciman The Display Browsing and Filtering of Graphtrees Daniel Tunkelang ALayout Algorithm for Undirected Graphs Stephen C North Drawing Ranked Digraphs with Recursive Clusters Ioannis G Tollis and Chunliang Xia Graph Drawing Algorithms for the Design and Analysis of Telecommunication Networks Michael Himsolt A View to Graph Drawing Algorithms through GraphEd C L McCreary C L Combs D H Gill and J V Warren An Automated Graph Drawing System Using Graph Decomposition Michael Junger and Petra Mutzel Maximum Planar Subgraphs and Nice Embeddings Practical Layout Tools Peter Eades and Xavier Mendonca Heuristics for Planarization by Vertex Splitting Takao Ozawa Planar Graph Embedding with a Specied Set of FaceIndependent Vertices Bjorn Sigurd Benestad Johansen Implementation of the Planarity Testing Algorithm by Demoucron Malgrange and Pertuiset Jo el Small A Unied Approach to Testing Embedding and Drawing Planar Graphs Hermann StammWilbrandt A Simple LinearTime Algorithm for Embedding Maxi mal Planar Graphs H de Fraysseix and P Rosenstiehl The LeftRight Algorithm for Planarity Testing and Embedding P O de Mendez Connexity of Bipolar Orientations New Developments in Geometric Graph Theory J Pach Abstract not Available Characterizing Proximity Trees y z Prosenjit Bose William Lenhart and Giusepp e Liotta Much attention has b een given over the past several years to developing algorithms for emb edding abstract graphs in the plane such that the resulting drawing has certain geomet ric prop erties For example those graphs which admit planar drawings have b een completely characterized and ecient algorithms for pro ducing planar drawings of these graphs have b een designed For an overview of graph drawing problems and algorithms the reader is referred to the excellent bibliography of Di Battista Eades Tamassia and Tollis More over many problems in pattern recognition and classication geographic variation analysis geographic information systems computational geometry computational morphology and com puter vision use the underlying structure present in a set of data p oints revealed by means of a proximity graph A proximity graph attempts to exhibit the relation b etween p oints in a p oint set Two p oints are joined by an edge if they are deemed close by some proximity measure It is the measure that determines the typ e of graph that results Many dierent measures of proximity have b een dened The relatively closest graph the relative neighb orho o d graph the gabriel graph the mo died gabriel graph and the delaunay triangulation are but a few of the graphs that arise through dierent proximity measures An extensive survey on the current research in proximity graphs can b e found in Jaromczyk and Toussaint As the survey suggests interest in proximity graphs has b een increasing rapidly in the last few years but most of the interest has b een algorithmic and little attention has b een given to the combinatorial characteristics of these graphs Monma and Suri show that any tree with maximum vertex degree ve can b e drawn as a minimum spanning tree We study the problem of drawing trees as certain typ es of proximity graphs We say that a tree T can b e drawn as a proximity graph when there exists a set of p oints in the plane such that the proximity graph of that set of p oints is isomorphic to T Some sucient conditions for such drawings to exist have b een given by Cimikowski for relatively closest graphs by Matula and Sokal for gabriel graphs and by Urquhart for relative neighb orho o d graphs However there exists no complete combinatorial characterization for any of the these typ es of proximity graphs To this end we give a complete
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