Dynamic Graph Drawin g Robert F . Cohen (Brown Univ ., USA ) Drawing graphs is an important problem that combines flavors of computational geometr y and graph theory . Applications can be found in a variety of areas including circuit layout , network management, software engineering, and graphics . The main contributions of thi s paper can be summarized as follows : (i) We devise a model for dynamic graph algorithms , based on performing queries and updates on an implicit representation of the drawing, an d we show its applications . (ii) We present several efficient dynamic drawing algorithms fo r trees, series-parallel digraphs, planar st-digraphs, and planar graphs . These algorithms adop t a variety of representations (e .g ., straight-line, polyline, visibility), and update the drawin g in a smooth way. (iii) We show that the implicit representation of the layout used by ou r algorithms for trees and series-parallel digraphs also supports point-location and windo w queries. (Joint work with P . Bertolazzi, G . Di Battista, R . Tamassia, and I .G . Tollis .) A New Method for Planar Graph Drawings on a Gri d Goos Kant (Utrecht Univ ., The Netherlands ) We introduce a new method to optimize the required area, minimum angle and number o f bends of planar drawings of graphs on a grid . The main tool is a new type of orderin g on the vertices and faces of triconnected planar graphs . With this method linear time an d space algorithms can be designed for many graph drawing problems . (i) We show that every triconnected planar graph G can be drawn convexly with straight lines on an (2n ”4) x (n ”2) grid . (ii) If C has maximum degree four (three), then G can be drawn orthogonal with a t most [32 j + 3 (at most B.] + 1) bends on an n x n grid (Pi] x [21 grid, respectively) . (iii ) If G has maximum degree d, then G can be drawn planar on an (2n ” 6) x (3n ” 6) grid with minimum angle larger than d 2 radians and at most 5n ” 15 bends . These results give i n 1 some cases considerable improvements over previous results, and give new bounds in othe r cases . Several other results, e.g. concerning visibility representations, are included . An Automatic Layout Facilit y Giuseppe Liotta (Univ . Rome, Italy ) An automatic layout facility is a tool that receives as input a graph-like structure and i s able to produce a diagram that nicely represents such a structure . Because of the increasin g number of systems that manage diagrams, automatic layout facilities and algorithms fo r graphs layout have been extensively studied in the last years . We present a new approach i n designing an automatic layout facility . Our approach is based on a modular management of a collection of algorithms and on a tool that is able to automatically select the best algorith m for a given application . Such approach has been used for devising the automatic layout facilit y of Diagram Server, a network server that offers to its clients several facilities for managin g diagrams . (Joint work with P. Bertolazzi and G . Di Battista .)

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