### Table 12. Interaction of lexical, syntactic and semantic information in KPs.

2004

"... In PAGE 10: ... Semantic information in KPs. KP Semantic Link Semantic category Expected variations is a amp;home for Synonymy Home house, living-place, roof are ^colour Hypernym Colour brown, blue, green is a ^time when Hypernym Time period, moment is an amp;amount of Synonymy Amount Quantity Although each kind of token has a value when used alone Table12 shows some possible interactions, and this is that type of search that would include lexical, syntac- tic and semantic information, providing a quite flexible way of getting access to ... ..."

### TABLE 44.3.3 The time complexity of some fundamental graph drawing problems: trees. k is a xed constant k 1. CLASS OF GRAPHS PROBLEM TIME COMPLEXITY tree draw as the Euclidean minimum span- ning tree of a set of points in the plane NP-hard

### Table 1.8: The time complexity of some fundamental graph drawing problems: trees. We denote with k a xed constant such that k 1. Class of Graphs Problem Time Complexity Source tree draw as the Euclidean minimum spanning tree of a set of points in the plane

1997

Cited by 14

### Table 5.1: The equations to calculate the values of width for a node and the values of reference and level for the children 1; . . .; d of . We show that the calculations of these attributes can be maintained by storing T as a linear attribute grammar (see section 3.4). Lemma 5.2 Using the equations in table 5.1, the attributes width, level, and reference for the 2-drawing of a tree T can be maintained as a linear attribute grammar. Proof: Consider a node of T. The only synthesized attribute of is width( ). The inherited attributes are level( ) and reference( ). By de nition 3.19, we need to show that the precedence graph G of T is acyclic and all dependencies are linear.

### Table 1: Drawing Performance. We show two performance measures for our drawing and culling algorithm: the time to draw the scene with vs. without culling, and the number of nodes drawn (with culling). Our new method achieves a near-constant drawing time for any size tree. Note that for the largest tree, we are not able to enqueue all nodes in the tree as the size of the vector grows too large for the applica- tion to t in main memory.

"... In PAGE 5: ... Both drawing and culling are now based entirely on tree topology, and do not depend on any properties of Grid- Cells. In addition, there is now little bene t to drawing items in order of importance , because our drawing algo- rithm requires a nearly constant amount of work after the dataset size surpass a particular point ( Table1 ). We elimi- nate the extreme performance penalty of updating a sorted queue of items to be drawn, instead using a simple FIFO.... ..."

### Table 1 Area-requirements for planar grid tree drawings. not vertices of G. ? is an orthogonal drawing (see Fig. 1.c) if each edge is a chain of alternating horizontal and vertical segments. A grid drawing is such that the vertices and bends along the edges have integer coordinates. Planar drawings, where edges do not intersect, are especially important because they improve the readability of the drawing, and, in the context of VLSI layouts, they simplify the design process [2, 19, 28]. An upward drawing of a directed graph is such that every edge is a curve monotonically nondecreasing in the vertical direction (when traversed along the direction of the edge).

1996

Cited by 12

### Table 5: Tree options

"... In PAGE 79: ...xx(btex This is a new root etex); newTree.x(xx)(ff); drawObj(x); Tree options Table5 shows which options are supported by a Tree. A Tree constructor also accepts connection options (see section 5.... ..."

### Table 7.4 schematically compares the known results on weak fl-drawability against those on strong fl-drawability for the family of trees. Each row corresponds to a difierent interval of fl and reports the maximum vertex degree k that a tree can have to admit a strong or weak fl-drawing for some values of fl in the interval. Of particular interest is the value fl = 2, where a remarkable difierence in the family of drawable trees can be noticed depending on whether the region of in uence is assumed to be an open set (in which case it coincides with the relative neighborhood region) or a closed set (in which case it coincides with the relatively closest region).

### Table 4. Average misclassification rate and tree size of all artificial data sets per ratio of nonmonotonicity. The column Frac. Mon. gives the fraction of monotone trees generated by the standard algorithm.

"... In PAGE 10: ...Table4 summarizes the results of our experiments with the artificial data sets. Each artificial data set was generated by making random draws from a pre- specified tree model.... ..."

Cited by 1

### Table 3: Schematic Architecture of WinKE In the data layer information about the tree structure is stored in the Tree Database. Parallely the Graphics Database contains a graphical description of the currently displayed proof tree. That description can be calculated directly given the information from the Tree Database by applying the tree drawing algorithm mentioned before. The middle layer is the so-called internal layer. This is where the actual computations take place. The Internal Graphics Manager takes the infor- mation from the Graphics Database and passes it on to the Graphic Window Manager, which nally displays it on the screen. User inputs that directly a ect the graphics come either through the Graphic Window Manager (e.g. mouse clicks) or the Tool Manager to the Internal Graphics Manager. The Internal Graphics Manager informs the Tree Manager about such events. 19

"... In PAGE 18: ... 5.3 System Architecture In Table3 a schematic representation of the architecture underlying WinKE is given. The system can be seen as divided into three layers.... ..."