# Questions tagged [prims-algorithm]

Prim's algorithm is a greedy algorithm which forms minimum spanning tree for the given graph. During execution, Prim's algorithm grows single tree by adding edges to it, unlike Kruskal's algorithm in which there can be multiple minimum spanning trees during execution.

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### MST with weights in {1, 2, 3, 4, 5}

I am given an undirected connected graph with $n$ nodes, average degree $\sqrt{\log n}$, and each edge having integer weight in $\{1,..,5\}$. I am asked to describe MST algorithm which is as efficient ...
1 vote
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### How to find if there's an MST where vertex $v$ has degree 2 in it? [duplicate]

I've faced this question and I hope that someone can help with it. Question: We're given an undirected graph $G=(V,E,w)$ where $w\colon E\rightarrow \mathbb{Q}$ and vertex $v$. We want to find if ...
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### Why do basic graph algorithms (BFS, DFS, Prim, Kruskal) have a similar structure?

This is my first post on CS Stack Exchange. For some time, I have been studying basic graph algorithms, mainly BFS, DFS, minimum spanning trees and their basic algorithms (Kruskal and Prim). One thing ...
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### Minimum unrooted binary spanning tree

Given a graph $G$ with $n$ tip vertices, $n-2$ internal vertices, and a cost on each edge $C(v)$, find a minimum spanning tree subject to degree constraints: tips have a degree of $1$ internal ...
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### MST - Every edge visited once

I know that every vertex is visited exactly once but In Prim’s algorithm to find the MST, does every edge of the input graph is checked exactly once?How do I prove this? Although this look false but ...
1 vote
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### The Cut Lemma for graphs with non-distinct edges

In my introductory algorithms class I recently learned about the Cut Lemma and how it can be used to prove correctness for many Minimum Spanning Tree algorithms like Kruskal's and Prim's. In class, to ...
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### Find MST on grid graph with only weight of 1 and 2 in $O(|V|+|E|)$

Given a grid graph $G=(V,E)$ which has only two different integer costs/weights of 1 and 2. Find Minimum Spanning Tree in $O(|V|+|E|)$. I tried the following: Changing Kruskal using a counting Sort ...
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### Best algorithm (Time Complexity) to find Minimum spanning tree of an complete, positive weighted, undirected, graph

Suppose that we have a complete undirected positive weighted graph $G = \langle V, E\rangle$. What is the most efficient algorithm, in terms of time complexity, to find an MST for $G$? The best prime ...
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### Improve Prim's algorithm runtime

Assume we run Prim’s algorithm when we know all the weights are integers in the range {1, ...W} for W, which is logarithmic in |V|. Can you improve Prim’s running time? When saying 'Improving', it ...
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### Minimum Spanning Tree with one particular edge minimised(continued)

I have recently encountered a coding problem, specifically, the CCC problem S4. In the problem, it states that you are given a spanning tree, or otherwise a "valid plan of pipes", that connect each ...
1 vote
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### Minimum spanning tree such that one edge can be minimised

During a computer coding exam, I have encountered such a problem. Given a list of vertexes and edges between the vertexes,and a positive number, D, what is the minimum spanning tree between the ...
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### MST: Is there such an example of a graph with unique mst and not unique light edge?

The problem is the following: Give an example of a graph that has a unique minimum spanning tree but for every cut of the graph, there is not a unique light edge crossing the cut. I am trying to ...
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In the CLRS, time complexity of Prim's algorithm is $O(|V|lg|V|+|E|lg|V|)=O(|E|lg|V|)$. But, for my understanding, Prim's algorithm iterates $|E|$ times for DECREASE-KEY operation which takes $O(lg|V|... 1 vote 1 answer 5k views ### Minimum spanning tree - Prim's algorithm I have to demonstrate Prim's algorithm for an assignment and I'm surprised that I found two different solutions, with different MSTs as an outcome. Now I now that shouldn't happen, so I wonder what I ... 1 vote 0 answers 120 views ### n'th cheapest MST in a graph, with multiple edges that can have the same weight I'm trying to think about an algorithm for this problem. I know there is an algorithm for the second cheapest MST in a graph, but if I understood it correctly it only solves cases in which every ... 1 vote 2 answers 7k views ### Time complexity of Prim's algorithm There is this Prim's algorithm I am studying, the time complexity of which is$O(n^2)$(in the adjacency matrix). As far as I have understood,that is because we have to ckeck all the nodes per every ... 2 votes 1 answer 1k views ### MST for a finite number of weights Let$F$be a finite set of real numbers say$\{w_1,\dots,w_k\}$. Let$G=(V,E)$be an undirected connected graph and let$w\colon E\to F$be a weight function. Describe a linear time algorithm that ... 3 votes 2 answers 441 views ### Minimum path - robot motion problem combined with freeze tag problem Alright, I am not entirely sure if this is the right place to ask this, but here goes: I have a map of coordinates of robots and obstacles. The first robot is awake from the start of the problem and ... 1 vote 1 answer 686 views ### Prim's algorithm on graph with weights of only$1$and$2$on each edge I have this version of Prim's algorithm Prim$(G=(V,E),s\in V,w)\\ 1.\ d(s)\leftarrow 0;\forall u \neq s:d(u)\leftarrow \infty\quad \color{red}{O(|V|)}\\ 2.\ \forall u \in V:p(u)\leftarrow \text{...
Let $G=(V,E)$ which is undirected and simple. We also have $T$, an MST of $G$. We add a vertex $v$ to the graph and connect it with weighted edges to some of the vertices. Find a new MST for the new ...