Models of random spanning trees
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908995998973952 |
|---|---|
| author | Babson, Eric Duchin, Moon Iseli, Annina Poggi-Corradini, Pietro Thurston, Dylan Tucker-Foltz, Jamie |
| author_facet | Babson, Eric Duchin, Moon Iseli, Annina Poggi-Corradini, Pietro Thurston, Dylan Tucker-Foltz, Jamie |
| contents | There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges and then employ a greedy algorithm to choose the minimum-weight spanning tree (MST). Though MST is a workhorse in applications, the mathematical properties of random MST are far less explored than those of UST. In this paper we develop tools for the quantitative study of random MST. We consider the standard case that the weights are drawn i.i.d. from a single distribution on the real numbers, as well as successive generalizations that lead to \emph{product measures}, where the weights are independently drawn from arbitrary distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Models of random spanning trees Babson, Eric Duchin, Moon Iseli, Annina Poggi-Corradini, Pietro Thurston, Dylan Tucker-Foltz, Jamie Discrete Mathematics Combinatorics Probability 05C05 G.2.2 There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges and then employ a greedy algorithm to choose the minimum-weight spanning tree (MST). Though MST is a workhorse in applications, the mathematical properties of random MST are far less explored than those of UST. In this paper we develop tools for the quantitative study of random MST. We consider the standard case that the weights are drawn i.i.d. from a single distribution on the real numbers, as well as successive generalizations that lead to \emph{product measures}, where the weights are independently drawn from arbitrary distributions. |
| title | Models of random spanning trees |
| topic | Discrete Mathematics Combinatorics Probability 05C05 G.2.2 |
| url | https://arxiv.org/abs/2407.20226 |