This Repository implements experiments for finding a Spanning Tree with Low Crossing Number
- The input is: set of points P (n=|P|) and optional a set of lines L
- An algorithm for this problem outputs: set of edges F forming a spanning tree for P with crossing number t
- t is the maximum crossing number of any line in L
This project is released under the MIT license.
- Python 2.7
- NumPy for efficient computation
- matplotlib for plotting
- Gurobi solving LPs
-
Install the above libraries as they are not preinstalled
$ sudo apt-get install python-numpy python-matplotlib -
Check if the current Gurobi license is activated. A correct prompt looks like this
$ gurobi.sh Python 2.7.2 (default, Nov 21 2011, 12:59:35) [GCC 4.2.4 (Ubuntu 4.2.4-1ubuntu4)] on linux2 Type "help", "copyright", "credits" or "license" for more information. Gurobi Interactive Shell (linux64), Version 5.1.0 Copyright (c) 2013, Gurobi Optimization, Inc. Type "help()" for help gurobi> -
Clone the repository
$ git clone https://github.com/komax/spanningtree-crossingnumber
Two command line tools were developed:
- Executation of a single experiment
- Generation of csv files
An experiments consists of these parameters
- generation of uniform or grid data
- reading data from a file
- controlling sampling of lines
- selecting a solver
- specification of the output
The outputs for an single experiment are
- Standard Output in form of text information
- dumping the graph as png file
- open the GUI from matplotlib to browse the spanning tree
The csv tool dumps only the text information (crossing number, size of the points, number of lines, ...)
An experiment has the following flags:
$ ./experiment.py -h
usage: spanning_tree_with_low_crossing.py [-h]
[-s {hp_lp,fekete_lp,cc_lp,mult_weight,opt,all}]
[-d DIMENSIONS] [-n NUMBER]
[-g {uniform,grid}] [-i INPUT]
[-l {all,stabbing,random}] [-m MEAN]
[-p] [-r] [-v]
run an parameterized experiment to compute a spanning tree with low crossing
number
optional arguments:
-h, --help show this help message and exit
-s {hp_lp,fekete_lp,cc_lp,mult_weight,opt,all}, --solver {hp_lp,fekete_lp,cc_lp,mult_weight,opt,all}
choose an algorithm computing a feasible solution
-d DIMENSIONS, --dimensions DIMENSIONS
number of dimensions of point set
-n NUMBER, --number NUMBER
quantify how many points you want
-g {uniform,grid}, --generate {uniform,grid}
how should the point set be sampled
-i INPUT, --input INPUT
specify a input file
-l {all,stabbing,random}, --linesampling {all,stabbing,random}
structure of the line set
-m MEAN, --mean MEAN run experiment m times and returns averaged results
-p, --plot plots the computed solution into a widget
-r, --record record computed solution into a png
-v, --verbose adds verbose outputs to STDOUT
An example usage is
$ ./experiment.py -n 16 -g grid -l stabbing -s mult_weight -r -v
Start generating graph...
Graph has been created.
Sampling of lines started...
Sampling of lines finished.
Start now computing a spanning tree...
Computing a spanning tree finished.
CPU time (in sec) 2.64830684662
crossing number=5
iterations=15
number of points=16
number of lines=120
all crossings=330
average crossing number=2.75
Start now plotting...
Closed plot.
The flags the flags for generating a csv file are almost the same, except the
specification for range 4..20 and stepping by --increment 2:
$ ./csv_experiment.py -f 4 -t 20 --increment 2
-c generates a human readable header prepending the csv file. Use this flag
for understanding the file format or consult the generated results in the
directory results