that are optimal with respect to both the time complexity and to the area achieved . Several results show that while series-parallel digraphs have a rather simple and well understoo d combinatorial structure, naive drawing strategies lead to drawings with exponential area , and clever algorithms are needed to achieve optimal area . Angular Resolution of Straight-Line Drawing s Michael Kaufmann (Universitat Passau and Max-Planck-Institut Saarbrucken, Germany) The angular resolution of a drawing of graph G is the minimum angle between two inciden t edges that appears in the drawing . In this talk the state of the art is presented how t o maximize the angular resolution . First the general technique by Formann et al . [FOCS'90] is reviewed, then a refinement for planar graphs is given . A recent paper of Malitz/Papakosta s [STOC'92] shows that planar graphs can be drawn planar with minimum angle only depending on the maximum degree of the vertices . At the end, some aspect on the relationship of resolution and area are discussed . Algorithms for Orthogonal Drawing s Roberto Tamassia (Brown Univ ., USA ) An orthogonal drawing of a graph is such that the edges are represented by polygonal chain s consisting of horizontal and vertical segments . The intermediate vertices of the chain (whic h are not vertices of the graph) are called bends . In this talk we survey algorithms for construct ing planar orthogonal drawings . The main quality measures considered are the minimizatio n of the number of bends and of the area of the drawing . The construction of planar orthogonal drawings has many important applications, including graph visualization, VLSI layout, facilities floorplanning, and communication by light or microwave . Given an embedded plana r graph G with n vertices, a planar orthogonal drawing of G with the minimum number o f bends can be computed in 0(n 2 log n) time using network-flow techniques . Drawings wit h 0(n) bends can be constructed in 0(n) time using visibility representations . Also, there ar e families of graphs that require f2(n) bends . Open problems include minimizing bends ove r all possible embeddings, and finding an efficient parallel algorithm for bend minimization . Circle Packing Representation in the Plane and Other Surface s Bojan Mohar, (Univ. of Ljubjana, Slovenia) The Andreev-Thurston circle packing theorem is generalized and improved in three ways . First, to arbitrary maps on closed surfaces . Second, we get the simultaneous circle packin g of the map and its dual map so that, in the corresponding straight-line representations of th e map and the dual, any two edges dual to each other cross at the right angle . The necessar y and sufficient condition for a map to have such a primal-dual circle packing representatio n is that its universal cover is 3-connected (the map has no "planar" 2-separations) . Finally, a polynomial time algorithm is obtained that given a map M and a rational number E > 0 finds an c-approximation for the primal-dual circle packing representation of M . In particular, we get a polynomial time algorithm for geodesic convex representations of reduced maps o n arbitrary surfaces .

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