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Questions tagged [spanning-trees]

The spanning tree of a connected undirected graph G is a tree having all the vertices and some number of edges of G.

18 questions with no upvoted or accepted answers
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6
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712 views

Minimum vertex-weight directed spanning tree where the weight function depends on the tree

Given a directed graph $G=(V,E)$ and a node $r\in V$, I need to grow a tree $T$ rooted at $r$ that has a minimum weight and spans all reachable nodes in $G$. The weight function assigns a non-...
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0answers
149 views

MST that contains a shortest $s,t$-path

Consider the problem in which we have an (undirected) graph $G=(V,E)$, weight function $w:E\to\mathbb N$ and a pair of vertices $s,t\in V$, and are required to determine whether there exists an MST $T$...
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1answer
102 views

Survival algorithm for Network deterministic failures

Consider an undirected network $G = (V,E)$ in which edge $e$ $\in$ $E$ fails after (deterministic) time $t(e) > 0$. Network failure occurs at the first instant in which $G$ is no longer connected. ...
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4k views

Applications of min spanning trees

What are the significant applications of minimum spanning trees? After doing some research online and in several textbooks, I have found three real-world applications: Building a connected network. ...
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0answers
51 views

Form a Tree having minimum diameter

I am given a connected graph. I have to construct a spanning tree from the graph, that has minimum diameter. However, I looked for the solution, and the solution goes like this. If the diameter of ...
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0answers
97 views

Build transportation system to travel between cities

Given $n$ cities, I'm looking to build a transportation system that allows travelling between every two cities. For every two cities $i$ and $j$, a road can be paved in the cost of $c_{ij}$. Also, ...
1
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0answers
53 views

Spanning tree with equally separated edge weights

I have a fully-connected graph $G=(V,E)$ with edge weights $w(v)\in\mathbb{R};v\in V$ and I need to find a spanning tree $T=(V_t\subseteq V,E_t\subseteq E)$ where the set of edge weights in the tree ...
1
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1answer
138 views

Choosing spanning trees to maximise node connectivity

Given: n variables in X, and m sets of variables where each set, Ci contains a subset of X. I am trying to generate the graph G = (X, E) by picking the edges in E given the following constraints. ...
0
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1answer
39 views

Average branching factor of an undirected graph

I'm trying to determine, given an unweighted undirected graph, the maximum number of leaves of any travelling of the graph, which means, the maximum number of leaves among all traversals of every ...
0
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0answers
11 views

Is Edmonds' Matroid partitioning algorithm optimal w.r.t lexicographical order?

We all know that, given a matroid $(E, \mathcal{I})$, Edmonds' Matroid partitioning algorithm will result in a tuple of $E$-covering, pairwise-disjoint independent sets $(I_1, ..., I_k)$ with optimal (...
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0answers
14 views

Intuitively, my problem is a mix of perfect hashing, tree spanning, combinatorial stuff - Ordered Decision Tree?

The problem I'm trying to solve is difficult to to give a single name, but I'll call it the ordered decision tree problem. Imagine a row of commands: ...
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0answers
135 views

Spanning-Tree-Protocol and BFS? (Distributed Computing)

Given is graph with networks and bridges/switches. We know, the root Bridge is the bridge with the minimal Bridge-ID. The connections between every bridge and network is 1. In the lecture slides they ...
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115 views

Distributed MST in $O(n \log \log n)$

I'm facing the following problem: Describe a distributed MST algorithm in time $O(n \log \log n)$ I've managed to think of the following, Run GHS(Gallager, Humblet and Spira) algorithm, till there ...
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257 views

How to efficiently find a minimum spanning tree?

I found this question from CSLR that I'm trying to figure out before my final. You are given a weighted, connected, undirected graph G = (V, E) and one of its minimum spanning trees T ⊆ E. Now ...
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219 views

spanning tree of a DAG (directed acyclic graph) with less forward arcs

I am new to this algorithm and graphs. Just started learning. Could someone help me which algorithm is best suited to find the spanning tree of a Directed Acyclic Graph with less forward edges?
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51 views

two connected graph - find linear spanning subgrap such that subgraph is still connected

Graph $G$ is 2-connected. It means that for each two edges there are exists at least to disjont (in terms of edges) paths. Graph $G$ is not directed. Our task is to find spanning subgraph $H$ of ...
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76 views

Why if $G$ has two spanning trees $A$ and $A'$, then every edge of $A'\cup \{e_i\}\in A'$

Theorem: Let be $G$ a weighted graph in which every edge has a different weight. Suppose that $G$ has two spanning trees $A$ and $A'$. Let be $i$ the first index such that $e_i\ne e'_i$ ...
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2answers
4k views

Minimum spanning tree using DFS and BFS

Can we construct minimum spanning tree for an undirected graph with distinct weights using bfs or dfs? I have gone through many answers but each answer says something different and I am not convinced....