Commit 1a6b0e97 by Mario Surlemont

### Update todo.md

parent bde9332d
 ... ... @@ -31,9 +31,18 @@ - May implement My Ky's, even if it is not optimal/ 100% correct. Just to observe if there is a connection between symmetrical unconnected solutions and the runtime and how strong this connection is. (Possible indicators: runtime, number of lazily added constraints) ❌ - Unfortunately her symmetry breaker made use of edges and our model consists only of node variables. - Until now there has no symmetry breaker come to my mind and I haven't recognised one in a paper yet. ### runtime * Create random graphs and try to compare runtime between ILP and ASP. - Measure some characteristics of the graphs such as density, |V|, |E|, maximum degree, minimum degree, average degree, (maybe standard derivation of degree or median degree?) - Measure some characteristics of the graphs such as density, |V|, |E|, maximum degree, minimum degree, average degree, (maybe standard derivation of degree or median degree?) ✔ - The graphs have been tested on random graphs with different size (|V| = 10, 20, 50, 100, 250, 500) with each size having 10 density(0.1, 0.2, ..., 0.9) levels. - The results of this implementation were comparable to the one from _An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets*_. - On random graphs the implementation can handle much more vertices than on our graphs. - A fact that is *very* interesting is that on gridlike graphs the implementation performs way worse. Even when those graphs have similar density and much less vertices. - A major problem seems to be a low average degree and a low maximum degree of the nodes! - It seems to be as I assumed that when "high value" vertices are missing there are to many alternatives which have to be excluded in the iteration process. - I should create tables with the differences in characteristics of those gridlike graphs and random graphs. - On "thin" random graphs (width << length) the algorithm performs much better as there are not so many alterantive I assume. - Measure and note gap between |D| of a minimal connected and a minimal unconnected solution. Measure for each |D| number of unconnected solutions which were found(ILP-only) and how many constraints where added in sum. - Measure the time which was needed to find the first (nearly) optimal solution (strong upper bound) and the time needed to close the gap. * Make some more detailed tests and check for the following connections: ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!