* Read _An Efficient Branch and Cut Algorithm to Find Frequently Mutated Subnetworks in Cancer_ again with focus on symmetry breaking.
* Read through _An Integer Programming Approach for Fault-Tolerant Connected Dominating Sets*_ again and check for symmetry breaking or other constraints to tighten up the space of solutions. ✔
- I could not find anything about symmetry breaking or additional inequalities for the case k=d=1 (Which is standard MCDS). But the table of results was interesting because they also tested their implemenation for the case k=d=1 which then is equal to our ILP-formulation. Their results were not bad but unfortunately I could not find anything more detailed description of their test graphs. Only number of nodes and density is shown. But those two properties are not sufficient as my personal test on random graphs revealed.
- An interesting observation, according to their result tables is that their largest test graph(with lowest densitiy) which has 200 nodes has an optimal solution that consists of "only" 26 nodes whereas an optimal solution for our bigger-leaf test graph in the case k=1 consists of 24 nodes while the graph only has 70 nodes. Both graphs have approximately the same density. So their graph must have some nodes which have a higher value/degree such that adding those nodes generates a higher profit than adding others. So there is no equal alternative to adding this node. This reduces the number of iterations and (as one can see in the table of results) the number of lazily added constraints. As a consequence I assume that is in an important factor which reduces the runtime.
- An interesting observation, according to their result tables is that their largest test graph(with lowest densitiy) which has 200 nodes has an optimal solution that consists of "only" 26 nodes whereas an optimal solution for our bigger-leaf test graph in the case k=1 consists of 24 nodes while the graph only has 70 nodes. Both graphs have approximately the same density. So their graph must have some nodes which have a higher value/degree such that adding those nodes generates a higher profit than adding others. So there is no equal alternative to adding this nodes. This reduces the number of iterations and (as one can see in the table of results) the number of lazily added constraints. As a consequence I assume that is in an important factor which reduces the runtime.
