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arXiv · 2211.12348

Typical values of extremal-weight combinatorial structures with independent symmetric weights

Yun Cheng·Yixue Liu·Tomasz Tkocz·Albert Xu
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Abstract

Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common optimisation problems, we establish asymptotically tight bounds when the weights are independent copies of a symmetric random variable (satisfying a mild condition on tail probabilities), in particular when the weights are Gaussian.

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Yun Cheng, Yixue Liu, Tomasz Tkocz, Albert Xu. 2022-11-22. Typical values of extremal-weight combinatorial structures with independent symmetric weights. https://doi.org/10.37236/10237

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