Abstract s Applications of Graph Drawing to Software Engineerin g Carlo Batini (Univ . Rome, Italy ) In several application areas of software engineering intermediate and final products of th e design activity are represented by means of diagrams . Diagrams present several advantage s over other representations, since they are an aid to clear thinking (a diagram is better tha t a thousand words) . Diagrams are external representations of organization charts, data an d function schemas, structure of procedure calls, pieces of code, etc . A diagram is characterized by a meaning (the "piece of reality" it draws), and a syntax, expressed by : a graphic grammar , that defines the types of symbols and connections allowed, aesthetic criteria adopted i n drawing the diagram . an underlying diagram model (e .g. hierarchical, planar, connected , etc) . In software engineering tools, diagram are manipulated by several functions, such as beautification, modification, refinement, merging of several diagrams, animation, etc . Each one of such functions is characterized by specific algorithms needed for the final activit y of diagram drawing . E .g. when we beautify a diagram we are interested to achieve som e aesthetic criteria that were previously not respected ; when we refine a diagram into a mor e detailed one, we are interested to maintain monotonicity of shape . Producing incrementall y such a library by dynamically tailoring and merging paradigmatic algorithms, results in a new and interesting research area . Algorithms for Drawing Trees Peter Eades (Univ . Newcastle, Australia ) Several conventions for drawing rooted trees are discussed : classical drawings, tip-over drawings, inclusion drawings, and h-v drawings . In each convention, a number of algorithms an d complexity results are available. For free trees (no specific root), algorithms are mostly draw n from folklore . Radial drawings, spring drawings, and orthogonal drawings are discussed . Extremal Problems in Graph Drawin g Janos Pach (Hungarian Academy of Sciences ) A geometric graph (a convex geometric graph) is a pair (V, E), where V is a set of points i n the plane in general position (in convex position), and E is a set of segments connecting som e points in V . I survey many recent results in geometric graph theory with special emphasi s on the following questions . (A) What is the maximum number of edges a geometric grap h with n vertices can have without containing a given forbidden configuration (e .g., k pairwis e disjoint edges o k pairwise crossing edges, etc .)? (B) What is the largest number An) with the property that any geometric graph of n vertices contains either f(n) pairwise disjoin t edges or f(n) pairwise crossing edges? (C) What is the maximum number of sides of a cell i n a geometric graph with n vertices? Some generalizations to higher dimensions (for geometri c hypergraphs) are also considered . Visibility Representations of Planar Graph s Ioannis G . Tollis (Univ . of Texas at Dallas, USA ) Interesting representations of graphs result from mapping vertices into horizontal segment s

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