### Table 9.2: Solved STS matrix. The set of solved matrixes is equivalent to the PQ-Tree Algorithm solution.

### Table 1. The running times of functions related to planarity: The rst column shows the type of the input graph, the second column shows the time for the call BL PLANAR(G), the third column shows the time for the call BL PLANAR(G; K), the fourth column shows the time required to check the result of the computation in the third column, i.e, the time for the call Genus(G) == 0, if G is planar, and the call CHECK KURATOWSKI(G; K) if G is non-planar, the fth column shows the time for the call HT PLANAR(G), and the last column shows the time for the call HT PLANAR(G; K). The last call is only made when G is planar, since there there is no e cient Kuratowski nder implemented for the Hopcroft-Tarjan planarity test. The meaning of the rst column is as follows: P stands for a random planar map with n nodes and m uedges, P + K3;3 stands for a random planar map with n nodes and m uedges plus a K3;3 on six randomly chosen nodes, P + K5 stands for a random planar mao with n nodes and m uedges plus a K5 on ve randomly chosen nodes, MP stands for a maximal planar map with n nodes, and MP + e stands for a maximal planar graph plus one additional edge between two random nodes that are not connected in G. In all cases the edges of the graph were permuted before the tests were started. For each type of graph we used n = 2i 1000, m = 2i 2000 for i = 0, 1, and 2.

1998

"... In PAGE 3: ... The implementation of the former function is shown in Figure 1, the imple- mentation of the latter function is equally simple. Table1 shows the running times of several functions related to planarity. In this table BL PLANAR stands for the planarity test of Lempel, Even, and Cederbaum with PQ-tree data structure of Booth and Luecker, the embedding algorithm of Chiba et al.... ..."

Cited by 4

### Table 1: Algorithmic components and intermediate rep- resentations used by algorithms Bend-Stretch, Column, and GIOTTO in the automatic graph drawing facility of Diagram Server.

### Table 2. Constraints in traditional graph drawing.

"... In PAGE 4: ...2 Input Dependent Constraints The constraints in the previous section did not depend on the input. Input dependent constrains that are commonly used in traditional graph drawing [5, 13, 25] are listed in Table2 . Next we discuss the possibility to apply these traditional drawing constraints to the layouts of sequence diagrams.... In PAGE 4: ... Next we discuss the possibility to apply these traditional drawing constraints to the layouts of sequence diagrams. The first constraint in Table2 describes a need to place a given set of vertices to the center of the drawing. This need is justified since the center of a drawing is usually the most important and prominent place where vertices can be placed.... ..."

### Table 1: Some characteristics of graph-drawing algorithms.

1997

"... In PAGE 2: ...1 The Graph Drawing Algorithms We focus on the sub eld of graph drawing which is concerned with the automatic generation of aesthetically pleasing drawings for humans, as presented in [2], [17] and [10]. In Table1 we see some de ning characteristics of graphs, graph drawing, and graph-drawing algorithms. Graphs can be of many di erent types, be drawn in many di erent styles, with di erent aesthetic goals and di erent methods.... ..."

Cited by 4

### Table 1: Some characteristics of graph-drawing algorithms.

1997

"... In PAGE 2: ...1 The Graph Drawing Algorithms We focus on the sub eld of graph drawing which is concerned with the automatic generation of aesthetically pleasing drawings for humans, as presented in [2], [17] and [10]. In Table1 we see some de ning characteristics of graphs, graph drawing, and graph-drawing algorithms. Graphs can be of many di erent types, be drawn in many di erent styles, with di erent aesthetic goals and di erent methods.... ..."

Cited by 4

### Table 4. Commonly used aesthetic criteria for traditional graph drawing.

### Table 1. Upper Bounds for 2-D Orthogonal Graph Drawing

1999

"... In PAGE 3: ... Using a diagonal layout our algorithm produces 2-degree-restricted square-drawings. Table1 summarizes bounds for 2-D orthogonal graph drawing. Table 1.... ..."

Cited by 19

### Table 3 compares the encoding creation time of CPQE with that of NHE and BPE. The creation time of PQE and PE is the same as CPQE and BPE, respectively.

"... In PAGE 10: ...750 Mhz Pentium III, user time in Linux Table3 : Encoding creation time in milliseconds of different al- gorithms The comparison is not easy, since the algorithms were run on dif- ferent machines. Algorithm 1 was written in C++ based on the PQ-tree implementation of Leipert [27].... ..."

### Table 2.2: Examples of drawing conventions for graphs drawings.

2001