A randomly weighted minimum spanning tree with a random cost constraint
Abstract
We study the minimum spanning tree problem on the complete graph $K_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent copy of the random variable $U^\gamma$ where $\gamma\leq 1$ and $U$ is the uniform $[0,1]$ random variable. There is also a constraint that the spanning tree $T$ must satisfy $C(T)\leq c_0$. We establish, for a range of values for $c_0,\gamma$, the asymptotic value of the optimum weight via the consideration of a dual problem.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.01229
- arXiv:
- arXiv:1905.01229
- Bibcode:
- 2019arXiv190501229F
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- Electron. J. Combin. 28 (2021), no. 1, Paper No. 1.22,-25