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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0answers
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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-...
4
votes
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 $T$...
3
votes
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. ...
3
votes
0answers
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. ...
1
vote
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 ...
1
vote
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
vote
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
vote
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
votes
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
votes
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 (...
0
votes
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:
...
0
votes
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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?
0
votes
0answers
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 ...
0
votes
0answers
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 $e_i\ne e'_i$ ...
-1
votes
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....
