Graph Drawing Software by Michael Jünger, Petra Mutzel

By Michael Jünger, Petra Mutzel

After an creation to the topic zone and a concise therapy of the technical foundations for the next chapters, this booklet positive factors 14 chapters on cutting-edge graph drawing software program platforms, starting from basic "tool boxes'' to personalised software program for numerous functions. those chapters are written through top specialists: they stick with a uniform scheme and will be learn independently from one another. The textual content covers many commercial purposes.

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There are four necessary and sufficient conditions for an orthogonal representation H to be a valid shape description of some 4-planar graph: (PI) There is a 4-planar graph whose planar embedding II is identical to that given by H restricted to the e-fields. We say that H extends II. (P2) Let rand r' be two elements in H with er = er , . Since each edge is contained twice in H these pairs always exist. Then string Sr' can be obtained by applying bitwise negation to the reversion of Sr. (P3) Let Islo and lsi 1 denote the numbers of zeroes and ones in string s, respectively.

A4) A tree and its mirror image are drawn identically up to reflection. (A5) Isomorphic subtrees are drawn identically up to translation. Technical Foundations 23 For a vertex v E V let Tz(v) be the subtree rooted at the left child of v, if it exists, else 11(v) = (0,0), and let Tr(v) be the subtree rooted at the right child of v, if it exists, else Tr(v) = (0,0). Basic traversal orders for the vertices of a binary tree T = (V, E) are defined by the following recursive functions: preorder(T) inorder(T) { { } if VeT) } i- 0 { if VeT) v = root(T); visit (v); preorder(11 (v)); preorder(Tr (v)); } } i- 0 { postorder (T) { i- 0 { v = root(T); postorder(Tz (v)); postorder (Tr (v ) ) ; visit (v); if VeT) v = root(T); inorder (11 (v )); visit (v); inorder(Tr (v)); } } The algorithm of Reingold and Tilford follows the divide and conquer principle implemented in the form of a postorder traversal of T = (V, E).

Basic traversal orders for the vertices of a binary tree T = (V, E) are defined by the following recursive functions: preorder(T) inorder(T) { { } if VeT) } i- 0 { if VeT) v = root(T); visit (v); preorder(11 (v)); preorder(Tr (v)); } } i- 0 { postorder (T) { i- 0 { v = root(T); postorder(Tz (v)); postorder (Tr (v ) ) ; visit (v); if VeT) v = root(T); inorder (11 (v )); visit (v); inorder(Tr (v)); } } The algorithm of Reingold and Tilford follows the divide and conquer principle implemented in the form of a postorder traversal of T = (V, E).

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