# A randomly weighted minimum arborescence with a random cost constraint

@article{Frieze2019ARW, title={A randomly weighted minimum arborescence with a random cost constraint}, author={A. Frieze and T. Tkocz}, journal={ArXiv}, year={2019}, volume={abs/1907.03375} }

We study the minimum spanning arborescence problem on the complete digraph $\vec{K}_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent uniform $[0,1]$ random variable. There is also a constraint that the spanning arborescence $T$ must satisfy $C(T)\leq c_0$. We establish the asymptotic value of the optimum weight via the consideration of a dual problem. The proof is via the analysis of a polynomial time algorithm.

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