Finding minimum spanning trees via local improvements
| Autor: | Addario-Berry, Louigi, Barrett, Jordan, Corsini, Benoît |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose total weight is at most $\rho$ by the minimum spanning tree (MST) on the same vertex set. Fix a non-negative random variable $X$, and consider this local search problem on the complete graph $K_n$ with independent $X$-distributed edge weights. Under rather weak conditions on the distribution of $X$, we determine a threshold value $\rho^*$ such that the following holds. If the starting graph (the "initial candidate MST") is independent of the edge weights, then if $\rho > \rho^*$ local search can construct the MST with high probability (tending to $1$ as $n \to \infty$), whereas if $\rho < \rho^*$ it cannot with high probability. Comment: 24 pages |
| Databáze: | arXiv |
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