\b0 is a modified version of 2DLab 2.0. In it, we (Mary, Bill and Renato) have added several algoritims that attempt to find a solution to the Travelling Sales
\i person
\i0 problem. We have also added a tour optimzer and changed the menus around. Version 3.0 is the result of a project for a graduate course in Mathematical Programming(CS720) in the Fall of 1991 at the University of Wisconsin-Madison. None of the functionality from version 2.0 has been changed. Below is the help text for version 2.0 amended in certain places for version 3.0.
2DLab
\b0 animates a few algorithms from computational geometry and combinatorial optimization. It was originally released in early 1990, back when I was a graduate student at Michigan State University. In the process of updating the program for 2.0, things changed substantially, and many features were added. I hope you like the program.\
\b Running the program
\b0 \
Two windows will appear when
\b 2DLab
\b0 is fired up. The Geometry Window\
contains the data and the results of any algorithms run on the\
data. The
\b 2DLab Control
\b0 window allows you to configure the data\
set, the algorithm, and the drawing that takes place.\
When the program is invoked, the
\b Drawing Window
\b0 will contain ten\
points, and the selected algorithm (Prim's MST algorithm by default)\
will be applied to these points. New points can be created by\
clicking in the window. There is a `margin' around the border of\
the window within which points will not be displayed, so If you\
click the mouse button and no point appears, you're probably too\
close to the edge (this margin was put in to make the Voronoi\
tesselation have a nice border.\
A new set of random points (uniformly distributed within the window's\
usable region) can be generated by entering the desired number of\
points in the editable text field and pressing the
\b Generate
\b0 button.\
The highlighted button in the RadioButton array in the
\b Control\
Window
\b0 identifies the particular algorithm to be `animated.'\
\b Anim/Disp
\b0 button will run the appropriate animation when pressed.\
\b Disp
\b0 button will simply display the resulting data structure without\
animating. It only works when the data structure has already been previously\
computed (i.e. ya gotta
\b Anim
\b0 before you can
\b Disp
\b0 ).\
\b Auto-Go
\b0 checkbox specifies the program's behavior when new\
points are created with the mouse. If the box is checked, the\
selected algorithm is run immediately when a new point is added.\
The three
\b color wells
\b0 allow you to pick background, foreground,\
and highlighting colors. When the display is drawn, points and\
line segments appear in the foreground color. During animation,\
transient drawing is done using the highlight color. By default,\
these colors are white, black, and 67% gray, respectively. You\
can set them to anything you want using the standard color well\
tricks.\
\b line width slider
\b0 controls how thickly everything is drawn (both\
points and lines).\
The `
\b Status
\b0 ' item displays informative (?) messages about the\
progress of the algorithm currently being animated, the drawing\
taking place, etc.\
\b Document menu
\b0 allows you to save the current data set in a\
`generic' form, load a similarly-formatted file in for animation,\
and save the generated imagery as TIFF or EPS. The file format\
for the data is simple. The first number is the number of ordered\
pairs (%d), and the remaining numbers are the pairs (%f %f). The error\
checking for I/O is pathetic, so please feed
\b 2DLab
\b0 well-behaved data files.\
The Copy item of the Edit menu may be selected. It sticks the contents of\
the Geometry window in the pasteboard.\
\b Algorithms
\b0 \
In the following brief descriptions, N is the number of 2D points,\
and the O-notation refers to time complexity rather than space\
complexity. When the algorithms are invoked, those with quick eyes\
will notice some graphical razzle-dazzle as the data structure is\
constructed. After the algorithm has completed, the `resulting'\
data structure will remain in the window.\
- Prim's O(N^2) Minimal Spanning Tree (MST) algorithm.\
- Kruskal's O(E log E) MST algorithm. WARNING: the implementation\
in this program is NOT optimal (it's actually O(N^2)). Anybody\
who wants to hack together the priority queue stuff to implement\
the optimal algorithm is free to do so (lazy, that's me).\
- Jarvis' O(N log N) convex hull construction algorithm.\
- Graham's O(N log N) convex hull construction algorithm.\
for these last two algorithms was written by Seth Teller, who\
apparently used Fortune's netlib code as a basis).\
- my own Gabriel Graph construction algorithm (it uses the\
Delaunay triangulation as a starting point).\
- my own Relative Neighborhood Graph construction algorithm (again,\
using the Delaunay triangulation as a starting point).\
Those interested in the details of the algorithms should refer to\
Preparata and Shamos' book on computational geometry. Sedgewick's\
book also has covers geometric algorithms. The GG and RNG haven't\
been used much, and are a little harder to find in the literature.\
Consult Toussaint, `The relative neighborhood graph of a finite\
point set', Pattern Recognition 12, 261-268 for info about the RNG.\
The Gabriel graph was used in Matula and Sokal, `Properties of\
Gabriel Graphs Relevant to Geographic Variation Research and the\
Clustering of Points in the Plane', Geographical Analysis 12,\
205-222. However, I don't have either of those papers in my\
posession. This software was based on the discussion in Tuceryan\
and Chorzempa, `Relative Sensitivity of a family of closest-point\
graphs in computer vision applications', Pattern Recognition 24,\
361-374.\
\b Algorithms for 3.0
\f1\b0 :\
\f0 Stupid Neighbor: This is basically a test algorithm that connects point 0 to point 1, point 1 to point 2, and so on. It is useful for testing the tour optimizer, and seeing how bad an algorithm can be.(Bill Roth, 1991, previously unpublished)\
Cheapest Insertion: This algorithm finds the point that can be added with the least cost to the over all solution. (Salkin & Mathur, Foundations Of Integer Programming, 1989 North-Holland, p 683.)\
Nearest Neighbor: At a given point, an arc will be drawn to the nearest unvisited point in the graph. (Lawler, Lenstra, et. al., The Traveling Salesman [sic] Problem, 1985, Wiley and Sons, p 150.)\
Nearest Addition: Given a set of connected points, the point nearest to an existing arc will be added to the graph.( Lawler, Lenstra, et. al., The Traveling Salesman [sic] Problem,1985, Wiley and Sons, p 157.)\
Farthest Insertion: This algorithm finds the point farthest away from all of the points in the tour, and finds the best place to insert it. (Lawler, Lenstra, et. al., The Traveling Salesman [sic] Problem,1985, Wiley and Sons, p 226.)\
The tour optimization procedure comes from Salkin & Mathur, Foundations Of Integer Programming, 1989 North-Holland, p 690-93.\
\b About the authors.\
\b0 This program was written by:\
Patrick Flynn\
Assistant Professor\
School of Electrical Engineering and Computer Science\
Washingon State University\
Pullman, WA 99164-2752\
(flynn@eecs.wsu.edu)\
For Version 3.0:\
Mary Tork Roth "the Brains" (torkroth@cs.wisc.edu)\
Bill Roth "the Brawn" (roth@cs.wisc.edu)\
Dr. Renato De Leone "The Professor" (deleone@cs.wisc.edu)\
Computer Science Department\
University Of Wisconsin\
1210 West Dayton Street\
Madison, WI 53706\
If you find bugs, let us know.\
If you add functionality, let us know.\
If you like/hate it and just want to tell us, let us know.\
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