and edges into vertical segments drawn between visible vertex-segments . (Two parallel segments of a given set are visible if they can be joined by a segment orthogonal to them, which does not intersect any other segment.) Such representations are called visibility representations . These representations find applications in VLSI layout, algorithm animation, visual languages and CASE tools . We consider three types of visibility representations : (i) Weak visibility representation, if two vertices are adjacent then their corresponding segments mus t be visible . (ii) c-visibility representation, where vertices can be represented by open, closed , or semiclosed horizontal segments in the plane such that two vertices are adjacent if an d only if their associated segments are visible . (iii) Strong-visibility representation, where ver tices are represented by closed horizontal segments such that two vertices are adjacent i f and only if their corresponding segments are visible . We discuss various types of visibilit y representations of planar graphs on the plane, cylinder, and sphere . Partial Orders for Planarity and Drawings Hubert de Fraysseix, and Pierre Rosenstiehl (EHESS, France ) A bipolar orientation of a graph appears often in the algorithm literature as a first ste p for the generation of a particular drawing . Here the properties of bipolar orientations ar e systematically explored in terms of circuits, cocircuits, rank activities, Tutte polynomial , poset dimension, angle bipartition and max flow-min cut theorem . Efficient algorithms are described to list, generate or extend bipolar orientations for general graphs or plane ones , with or without constraints . (Joint work with Patrice de Mendez .) Drawing Compound Digraphs and its Application to an Idea Organize r Kozo Sugiyama (Fujitsu, Japan ) A compound digraph is a directed graph with both inclusion and adjacency edges and i s widely used in diverse fields . In this talk, first, a heuristic method for automatically drawin g a compound digraph is presented . Then, several graphic interface techniques which facilitat e the method in organizing ideas such as direct manipulation, animation, incremental editing , fish-eyes (focusing, abridgements), and utilization of curves are discussed . Finally, it is emphasized that interface issues are important as well as algorithmic aspects of graph drawing . (Joint work with K . Misue. ) Area Requirement s Giuseppe Di Battista (Univ . Rome, Italy ) An upward drawing of an acyclic digraph is a planar straight-line drawing with the additiona l requirement that all the edges flow in the same direction, e .g., from bottom to top . Th e literature on the problem of constructing upward drawings of important classes of digraph s is surveyed . First, it is show that there is a family of binary trees with n vertices requirin g f2(n log n) area for any upward drawing ; moreover, that bound is tight, i .e . each binary tre e with n vertices can be drawn with O(n log n) area . Second, motivated by the elegant H-tre e layout algorithm for constructing non-upward drawings of complete binary trees, an algorith m is presented for constructing an upward drawing of a complete binary tree with n vertices i n 0(n) area . This result is extended to the drawings of Fibonacci trees . Third, it is shown tha t the area requirement of upward drawings of series-parallel digraphs crucially depends on th e choice of planar embedding . Also, parallel and sequential drawing algorithms are presented

/lp/association-for-computing-machinery/partial-orders-for-planarity-and-drawings-abstract-pc4ObKwddr