The folder contains triangular nxk arrays with 2<=n,k<=10 using the TSPLIB-format.

The instances where generated as part of the master's thesis of Daphne Rohrssen 
written 2022 under the supervision of Stefan Hougardy at the University of Bonn. 

Some of these instances are very hard to solve exactly for GeoSteiner 5.1. 
For example the 4x9 instance with 36 vertices needs more than 10 days of CPU time. 
SCIP-JACK 2.1 solves this instance within 20 minutes. However, one should be aware 
of the fact that both codes have numerical problems and cannot guarantee optimality  
of the solutions. 

The triangular arrays are based on a grid of isosceles triangles that have base 
length x=5822 and height y=5042. Among all choices for (x,y) with
- x even integer,
- y integral, and
- x,y <= 10000,
this tuple yields the best approximation for the triangular grid. 


GeoSteiner can be applied as follows, assuming that geosteiner corresponds to the 
path to GeoSteiner (configured to use GMP and CPLEX), and 2<=n,k<=10:

${geosteiner}/lib_points < ./$triangular_instance_${n}x${k}.tsp | ${geosteiner}/efst -g -m 2 | ${geosteiner}/prunefst -t | ${geosteiner}/bb

This means that the following happens:
- GeoSteiner reads the problem instance (lib_points)
- FST generation with greedy heuristic and GMP level 2 (efst -g -m 2)
- FST pruning and printing the time needed to do this (prunefst -t)
- FST concatenation via branch-and-bound (bb)


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For more information about GeoSteiner, see http://geosteiner.com/