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Questions tagged [minimum-spanning-tree]

Use this tag whenever your question is related to minimum spanning tree (MST). An MST of a connected edge-weighted graph G is a spanning tree whose sum of edge weights is as small as possible. We usually assume $G$ is finite, simple and undirected.

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Are edges in a minimum spanning tree not heavier than respective edges in another spanning tree?

Let $G$ be an undirected connected weighted graph, and let $T$ be a minimum spanning tree of $G$ with edge weights: $w_1 \le w_2 \le ... \le w_{n-1}$. Now let $T'$ be some other spanning tree of $G$ (...
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1answer
47 views

Define the time complexity of Kruskal's algorithm as function

I am trying to define the time complexity of Kruskal's algorithm as function dependant on: the number of vertices V the number of edges ...
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1answer
128 views

Boruvka MST algorithm using doubly linked lists

I'm reading Sedgewick & Wayne's Algorithms book, and one of the questions in one of the chapters is the following: Develop an implementation of Boruvka's algorithm that uses doubly-linked ...
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1answer
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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....
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0answers
80 views

Minimum spanning tree and Hamiltonian path

For a graph $G(V,E)$, under what conditions is a minimum spanning tree of $G$ equal to a hamiltonian path on $G$? IS there any body of literature connecting these two?
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0answers
44 views

Worst Case Analysis of a Multivariate Recurrence of a Graph Algorithm

I have a graph algorithm that runs in: $$ T(n, m) = \begin{cases} c_1 & n \leq 2 \lor m = 1\\ T(n - i,\ m - j - k) + T(i, k) + c_2 m + c_3 n & m \leq (n-i)i\\ T(n - i,\ m) + T(i, m) + ...
3
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0answers
380 views

Learning automata for degree constrained minimum spanning tree problem

I'm trying to understand the algorithm described in "Degree constrained minimum spanning tree problem: a learning automata approach" (Javad Akbari Torkestani, The Journal of Supercomputing; April 2013,...
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0answers
77 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, ...
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0answers
67 views

n'th cheapest MST in a graph, with multiple edges that can have the same weight

I'm trying to think about an algorithm for this problem. I know there is an algorithm for the second cheapest MST in a graph, but if I understood it correctly it only solves cases in which every ...
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0answers
218 views

How can I modify Kruskal's algorithm to work with limited resources?

In Kruskal algorithm, I decided to use it to construct a minimum spanning tree for a set of N = 100,000 points. Since my hardware does not allow me to keep all the distances between pairs of points, I ...
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0answers
61 views

NP-hardness of Capacitated Minimum Spanning Tree and Price Collecting Steiner Tree on dag/tree

I am thinking about the NP-completeness of two graph problems on different graph structures. For example: The Capacitated Minimum Spanning Tree for graph is NP-hard. However, is the problem still ...
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0answers
332 views

Working of the GHS algorithm

Can someone explain the working of the GHS algorithm using the graph given below. GHS is a distributed algorithm for finding the Minimum Spanning tree of a graph. The description of which can be found ...
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0answers
26 views

Minimum spanning tree classification problem with adjacent neighbors

I am new to minimum spanning trees. But have used the last few days on a problem I think matches MST, but cannot really figure out the connection. The problem is a minimum cost problem where N ...
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0answers
55 views

How many roots are there in an undirected root

Given an undirected tree with 7 nodes how many roots would this tree have. My intuition tells me that because the tree is undirected it would either be 7 or 0. How would I solve this?
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0answers
39 views

N-Guest Table, Graph Problem

The Queen of England wants to organize a set of tables for n guests talking different languages. The tables have to be set in a way that every guest can speak to his neighbor on the right and his ...
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0answers
100 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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0answers
515 views

Using Prim's for finding minimum cost arborescence in a special setting

I have a complete graph G which is directed. In essence, a node is connected to all other nodes in the graph. Also, for every pair of nodes, say ...
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0answers
200 views

find all edges in a weighed tree that are heaviest edges in some cycle

Given an undirected graph $G=(V,E)$ and a weight function $w:E\to\{1,2,3,\dots,10\}$: Let $U\subseteq E$ the set of all edges $e\in E$ that has a cycle in $G$ such that the cycle contains $e$ and all ...