# What is minimum spanning tree problem explain with example?

## What is minimum spanning tree problem explain with example?

A minimum spanning tree is a special kind of tree that minimizes the lengths (or “weights”) of the edges of the tree. An example is a cable company wanting to lay line to multiple neighborhoods; by minimizing the amount of cable laid, the cable company will save money. A tree has one path joins any two vertices.

### Why the minimum spanning tree of a graph may not be unique?

If the edge weights are all positive, it suffices to define the MST as the subgraph with minimal total weight that connects all the vertices. The edge weights are all different. If edges can have equal weights, the minimum spanning tree may not be unique.

#### Which algorithm solve the minimum spanning tree problem?

This is the simplest type of question based on MST. To solve this using kruskal’s algorithm, Arrange the edges in non-decreasing order of weights. Add edges one by one if they don’t create cycle until we get n-1 number of edges where n are number of nodes in the graph.

Which algorithm gives best solution for MST?

Prim’s and Kruskal’s Algorithm are the famous greedy algorithms. They are used for finding the Minimum Spanning Tree (MST) of a given graph.

How is spanning tree different from minimal spanning tree?

If the graph is edge-weighted, we can define the weight of a spanning tree as the sum of the weights of all its edges. A minimum spanning tree is a spanning tree whose weight is the smallest among all possible spanning trees.

## What are the applications of minimum spanning tree?

Suppose you want to construct highways or railroads spanning several cities then we can use the concept of minimum spanning trees. Designing Local Area Networks. Laying pipelines connecting offshore drilling sites, refineries and consumer markets. To reduce cost, you can connect houses with minimum cost spanning trees.

### Can there be multiple minimum spanning trees?

A graph can have more than one MST in the case where both trees have the same overall weight but different paths to complete the tree.

#### Can we get multiple MST for the same graph?

Or can G also have multiple MSTs? The answer would, probably be no ; multiple STs are possible (depends on the graph), but, if each edge has a unique weight , only one MST will be possible.

What is MST problem?

The dynamic MST problem concerns the update of a previously computed MST after an edge weight change in the original graph or the insertion/deletion of a vertex.

What is MST in algorithm?

A Minimum Spanning Tree (MST) is a subset of edges of a connected weighted undirected graph that connects all the vertices together with the minimum possible total edge weight. To derive an MST, Prim’s algorithm or Kruskal’s algorithm can be used.

## How to find the second best minimum spanning tree?

Use Kruskal’s algorithm to find MST T of graph G.

• Sort the edges in O (ElogE) time (E-no.of edges) and find MST using Kruskal’s algorithm in O (E) time (No.of edges in MST = V-1 where V = no.of vertices
• For each edge in MST,temporarily exclude it from the edge list (so that we cannot choose it).
• ### How to find maximum spanning tree?

– Negate all edge weights and then apply the MST algorithm rule.That is, multiply the negative value (-1) to all edge weights. – Apply either Kruskal’s or Prim’s algorithm to find the minimum spanning tree. – The result of minimum spanning tree is the maximum spanning tree of the graph.

#### What are some properties of minimum spanning trees?

The number of vertices in the spanning tree would be the same as the number of vertices in the original graph. V` = V

• The number of edges in the spanning tree would be equal to the number of edges minus 1. E` =|V|- 1
• The spanning tree should not contain any cycle.
• The spanning tree should not be disconnected.
• What is the maximum spanning tree algorithm?

The graph doesn’t change, and Kruskal’s algorithm, the algorithm for finding the maximum spanning tree in a graph doesn’t care what the root is…it just wants to find the largest edge at each step that doesn’t produce a cycle. The number of maximum spanning trees in a graph G remains constant. Whether you start at C, B, and E, doesn’t matter.