Graph Drawing - Planar Directed

... Construct Upward Planar Drawings ■ Since an upward planar digraph is a subgraph of a planar st-digraph, we only need to know how to draw planar st-digraphs ■ If G is a planar st-digraph without ... (upward planar polyline drawings) Graph Drawing 57 Planar Drawings of Graphs and Digraphs ■ We can use the techniques for dominance drawings also for undirected planar graphs: ■ orient G into a planar ... Graph Drawing 51 Planar Directed Graphs Graph Drawing 52 Upward Planarity Testing ■ upward planarity testing for ordered sets has the same complexity as for general digraphs (insert...

... box inclusion drawings) ■ drawings of series-parallel digraphs (delta drawings) ■ drawings of planar acyclic digraphs (visibility drawings, upward planar polyline drawings) Graph Drawing 91 Tree ... Graph Drawing 73 General Directed Graphs Graph Drawing 74 Layering Method for Drawing General Directed Graphs ■ Layer assignment: assign vertices to ... layout graph grammars for which optimal graph drawings can be constructed in polynomial time: ■ H-tree layouts of complete binary trees ■ hv-drawings of binary trees ■ series-parallel graphs...

... Trade-off (area vs. angular resolution): ■ [Kant 92] Computing the optimal angular resolution is NP-hard. 1 n ρ O dlog d 3 -- -- - -- - -- - -    = A Ω c ρn ()= Graph Drawing 37 Planar Straight-Line ... Graph Drawing 32 Planar Undirected Graphs Graph Drawing 33 Planar Drawings and Embeddings ■ a planar embedding is a class of topologically equivalent planar drawings ■ a planar embedding ... constant) for all planar graphs? ■ can we efficiently compute an approximation of the optimal angular resolution? ρΩ 1 7 d -- -- - -   = Graph Drawing 38 Planar Orthogonal Drawings: Minimization...

... graphs admit planar drawings. A graph which admits a planar drawing is called a planar graph. b d Fig. 1.3 (a) A planar drawing, and (b) a non -planar drawing of the same graph. If ... algorithms for drawing planar graphs can be successfully used for drawing a nonplanar graph by transforming the nonplanar graph into a similar planar graph. Furthermore, drawings of planar graphs ... depicts a planar drawing and a non -planar drawing of the same graph. It is preferable to find a planar drawing of a graph if the graph has such a drawing. Unfortunately not all graphs...

... Graph Drawing 58 General Undirected Graphs Graph Drawing 59 Algorithmic Strategies for Drawing General Undirected Graphs ■ Planarization method ■ if the graph is nonplanar, make it planar! ... of the drawing algorithms for planar graphs e.g., GIOTTO [Tamassia Batini Di Battista 87] ■ Orientation method ■ orient the graph into a digraph ■ use one the drawing algorithms for digraphs ... [Eades 84] Graph Drawing 60 A Simple Planarization Method use an on-line planarity testing algorithm 1. try adding the edges one at a time, and divide them into planar (accepted) and “nonplanar”...

... Graph Drawing 0 Graph Drawing Tutorial Isabel F. Cruz Worcester Polytechnic Institute Roberto Tamassia Brown University Graph Drawing 1 Introduction Graph Drawing 2 Graph Drawing ■ ... Graph Drawing 3 orthogonal drawing bend Drawing Conventions ■ general constraints on the geometric representation of vertices and edges polyline drawing planar straight-line drawing Graph Drawing ... is the maximum vertex degree. ρ ≤ 2π d -- -- - - Graph Drawing 8 Aesthetic Criteria ■ some drawings are better than others in conveying information on the graph ■ aesthetic criteria attempt to characterize...

... StringAdministrator1-name : String-staffID : IntegerStaff-specialty : StringConsultant-title : StringReport1-name : StringClient1*-title : StringProject1***-name : StringHardware-name : ... diagrams were created byhand: low-effect (-) , middle-effect (0) and high-effect (+).To confirm that these diagrams had an appropriateamount of low-, middle- and high-effect of the aesthetics,and ... October2001.GANSNER, E., and NORTH, D. (1998): Improved force- directed layouts. Proceedings of the Graph Drawing Symposium 1998. Montreal, Canada, 36 4-3 73,Springer-Verlag.GREEN, T. and PETRE, M. (1996): Usability...

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... 1(N- )-( )-a (N- )-( ( - )-a)N-b 1 N-b 1 1(N- )-( d) (N- )-( ( -d )- )( -b )-( )-a ( -b )-( ( - )-a)( -b )-( d) ( -b )-( ( -d )- )(c- )-( )-a ((c- )-a)(c- )-( d) c-d 1(d)-a 1 (c- )-a(N-b )-( )-a (N-b )-( ( ... 1a-N-c--ba-b 1N-b 1c-b 1sub-path a. seq. val.NP 1( - )-a(c- )- ( -d )- (c-d )- (c- )-a( -d)-a(c-d)-c 1non-terminated node is the same as skipping all thegraphs inside the non-terminated ... that ‘(N- )-( d)-a’ and ‘(N- )-( ( - d)-a)’ are different elements. However, in the frame-work of the node skip and the attributes of the non-terminated node, ‘(N- )-( )-a’ and ‘(N- )-( ( - )-a)’are...

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