Fortalecimiento de la Infraestructura Productiva

We present a tool to get an intuitive understanding of the ply-number , as well as explore and examine given drawings. The graphical user interface of our tool is shown in Figure 3.5. The graph is drawn and every edge is represented as a straight line. For every vertex the ply-disk is drawn. The disks are presented as red

3.3 Program and Features

Figure 3.3: The same graph as in Figure 3.1 with 5 vertices and 5 edges is drawn with ply-number one. All edges have the same length, as the left component is an equilateral

triangle, and the distance between any two nodes_{≥ length of any edge. Note that no two}

ply-disks overlap each other.

Figure 3.4: The complete graph K60 is drawn on a circle. The ply-number meets the

theoretical upper bound of n₂ = 30. Note that we conjecture, that this is the best we can

circles with some opacity level, such that the user gets some visual feedback, since overlaps are presented in a darker color. Additionally, we indicate the regions with the maximum ply-number , which we call maximum ply-regions, by drawing blue dots at the intersection points of the ply-disks. If the user selects a vertex to move, the edges are colored in a way, that the user can quickly identify the longest edge incident to the selected vertex. In addition to the instant feedback the user will be informed by a color-switch that the longest edge regarding the selected vertex changed.

The user can load and save graphs, choose different built-in layout styles, and modify and inspect the drawing according to its ply-number . Modification of the drawing includes moving vertices, where the ply-disks are updated instantaneously. In that way the user can get instant feedback on the changes. The indicators for the maximum ply-regions are updated as well. On small to medium graphs the ply-number is updated on the fly. For large or highly symmetric graphs we provide the option to switch off the automatic update function. If the automatic update function is toggled off, the ply-disks are still updated but the ply-computation is stalled until the modification is finished. In this setting the indicators of the maximum ply-region will not update appropriately.

Since the maximum ply-regions are a local phenomenon, we allow the user to zoom into the view, and shift the view to focus on the desired region and observe the local changes. Note that local changes might influence the ply-disks of many adjacent vertices.

LOAD & SAVE

We allow to load any graph from two main file formats, the first file format is gml [57], which provides information on the coordinates for each node, as well as information on the representation of the vertices and edges. In our tool we do not allow the modification of these meta-data beside the coordinates in the plane. Edges might contain meta-data regarding the edge routing. Since the ply-number is strictly defined on straight-line drawings we discard this information. In the gml format, data is stored as a list of node objects followed by a list of edge objects, as indicated in Figure 3.6 and 3.7. We save our graphs in the gml format.

As a second supported file format we chose graphml [17]. This file format is based on the HTML syntax and contains similar types of meta-data like coordinates in the plane, information on the representation of vertices and edges. Even though in these examples the amount of information in the graphml format seems to be larger, both formats are able to store the same information. An example of a vertex and an edge is presented in Figure 3.8.

3.3 Program and Features

Figure 3.5: The graphical user interface of the ply-exploration tool. A graph with 30 vertices and 40 edges is drawn. The ply-number of this drawing is 4. Note that the ply-disks are drawn, as well as indicators where the maximum ply-number occurs. Ad- ditionally, one vertex in the center is marked, and the incident edges are marked blue, whereas the longest edge is yellow. The options a user can choose from are file, layout, zoom, mode and optimize.

ZOOM

For exploration and further analysis of a given drawing, we implemented a zoom function. It allows the user to focus on local parts in a big graph. For easy access this function is bound to the "+" or "-" button as well as the mouse wheel. The displayed part of the graph can be panned by using the left mouse button.

Additionally, the indicators for the maximum ply-regions keep a constant size on the screen, regardless of zooming. In that way, looking at a large graph, the user can observe the regions with the maximal ply-number . This feature is presented in the Figures 3.9 and 3.10, where the same drawing in different zoom levels is shown. To reset the zoom we implemented a function to fit the drawing to the view.

node [ id 0 label "0" graphics [ x 380.77130126953125 y 585.5761108398438 w 30.0 h 30.0 type "rectangle" fill "#CCCCFF" outline "#000000" ] ]

Figure 3.6: The representation of a vertex in gml format. The information contains the coordinates in the plane, as well as layout properties regarding the representation of the vertex. edge [ source 1 target 4 grapics [ fill "#000000" targetArrow "none" ] ]

Figure 3.7: The representation of an edge in gml format. The source and the target vertices are given. Note that we consider undirected graphs.

3.3 Program and Features

<node id="n5">

<data key="d0" > <y:ShapeNode>

<y:Geometry x="489.5" y="335.5" width="30.0"

height="30.0"/>

<y:Fill color="#FFFF00" transparent="false"/>

<y:BorderStyle type="line" width="1.0" color="#000000" /> <y:NodeLabel x="13.0" y="13.0" width="4.0" height="4.0"

visible="true" alignment="center"

fontFamily="Dialog" fontSize="12" fontStyle="plain" textColor="#000000" backgroundColor="#FFFFFF" modelName="internal" modelPosition="c" autoSizePolicy="content"> </y:NodeLabel> <y:Shape type="ellipse"/> </y:ShapeNode> </data> </node> ...

<edge id="e96" source="n89" target="n88"> <data key="d1" >

<y:PolyLineEdge>

<y:Path sx="0.0" sy="0.0" tx="0.0" ty="0.0"/>

<y:LineStyle type="line" width="1.0" color="#000000" /> <y:Arrows source="none" target="standard"/>

<y:BendStyle smoothed="false"/> </y:PolyLineEdge>

</data> </edge>

Figure 3.8: The representation of a vertex and an edge in graphml format. This data contains the coordinates of the vertex in the plane as well as layout properties of vertices and edges.

Figure 3.9: A binary tree with 300 vertices is drawn. The ply-number of this drawing is 7. Note that the indicators for the maximum ply-regions are observable. Note that the size does not change, when zooming on the two left indicators. This scene is shown in the next Figure 3.10.

Figure 3.10: A part of the drawing from Figure 3.9 is shown, namely the indicators for the ply-regions which admit the ply-number 7.