Sorry for the complicated name - this is a merit. Let me introduce a problem.
Context: I have the type of location network with which I want to partition.
Definition of the problem: I have an undirected weighted graph G = {V, E, w} with many vertices V, edges E and edge weights W. Edges exist between all vertices in V.
Now I have C = {C1 ... CN} loop sizes | C1 | ... | CN | ST amount | C1 | ... | CN | equal to the total number of vertices | V |. The Ci cycle estimate is the sum of the weights of all the edges involved in the path.
Finally, here is the goal: I would like to put all the cycles of C in G so that their combined scores are maximum with the restriction that no cycles in C intersect with each other.
So, in unprofessional terms: I would like to fill the graph with cycles of a certain length st, the global weight is optimal.
I take on this problem: this problem is at least NP-hard because it can be reduced to something like a packing problem or a Hamiltonian cycle.
The optimal solution is probably not even pseudopolynomial. I tried to formulate the problem in several ways (graphs), and this always leads to explosions in the state, so an approach with smooth 2D dynamic programming is probably not possible (correct me if I'm wrong).
, , , , . , , - , . "" - . | C |! * | V | "". | V | . (.. ), | C |. , | C | | C | - .
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