LetG= (V, E) be a graph. A vertex cover inGis a subset of verticesS, so thatfor every edge e= ab∈E, either a∈Sor b∈S. Now T= (V, E) be a tree with non-negative weights assigned to its vertices. Describe a linear time algorithm for computing a vertex cover of minimum weight. (Weight of a vertex cover is sum of vertex weightsinit.)You should define all necessary terms in your proposed solution, and clearly outline your algorithm.

Q: you think finding the "longest path" from p to q can be solved in polynomial time? Given

A: You can solve this using  DFS or applying BFS twice

Q: Consider the graph below. Use Prim's algorithm to find a minimal spanning tree of the graph rooted…

A:

Q: Assume that the Floyd-Warshall algorithm is applied on a directed graph H. The graph H is…

A: Answer the above question are as follows:

Q: ht find a path through the augmentation graph through which a flow of 30 can be added. It might,…

A: introduction : Hill climbing algorithm: The hill climbing algorithm is an optimization technique…

Q: I have an idea for a greedy algorithm to find the largest clique. First I with a vertex u, then I…

A: solution in below step

Q: Create an algorithm that, given a directed graph g = (v e) and a distinguished vertex s v, finds the…

A: A directed graph, also known as a digraph, is a type of graph in which the edges have a direction…

Q: Dijkstra's algorithm works because, on every shortest path p from a source vertex u to a target…

A: The Dijkstra algorithm finds a low cost method between two nodes. The cost of the route between node…

Q: Let G = (V, E) be an undirected and connected graph, where each edge (u, v) E E has a weight wt(u,…

A: The solution for the above given question is given below:

Q: To help jog your memory, here are some definitions: Vertex Cover: given an undirected unweighted…

A: The question of providing a reduction from the Minimum Vertex Cover (MVC) problem to the Minimum Set…

Q: 2. Provide an algorithm that finds the shortest simple path from s to t that works if no simple path…

A: Answer 2:- For a path from u to w passing through v, we just need to find paths from u to v and v to…

Q: Write algorithm LargestShortestWeight(G, s,t)  pre-cond: G is a weighted directed (augmenting)…

A: given data: pre-cond: G is a weighted directed (augmenting) graph. s is the source node.t is the…

Q: Throughout, a graph is given as input as an adjacency list. That is, G is a dictionary where the…

A: Pseudocode is a way of describing an algorithm in a human-friendly format that doesn't have to…

Q: Brad is provided with a graph containing X branches. And it's given that the xh branch has a weight…

A: Introduction: Here, in this question, we have to write a Python code which finds the number of…

Q: Brad is provided with a graph containing X branches. And it's given that the xth branch has a weight…

A: Introduction: Here, in this question, we have to write a Python code that finds the number of…

Q: Write a function that returns true (1) if there is an edge between two vertices u and v in an…

A: Since you are not mentioning the programming language, here we are using C++ to complete the…

Q: H Suppose we run the Floyd-Warshall transitive closure algorithm on this graph. What is one edge…

A:

Q: Let G = (V, E) be a directed graph, and let wv be the weight of vertex v for every v ∈ V . We say…

A: Please refer to the following step for the complete solution to the problem above.

Q: Suppose you are given an undirected simple graph G(V, E). Design an efficient algorithm to determine…

A: To determine whether a given undirected simple graph G(V, E) is a tree or not, we can use a…

Q: given n−1 integers a2,… ,an and a tree with n vertices established at vertex 1. The leaves are all…

A: Here have to determine about the vertices established at vertex programming problem statement.

Q: ights are distinct. Is th

A: The statement is true.

Q: 50 10 F 10 40 B 20 10 20 A 80 50 (D 90 20 E 30G 20 )

A: Dijkstra's algorithm has many variants but the most common one is to find the shortest paths from…

Q: As described in the reading and lecture, an adjacency matrix for a graph with n vertices number 0,…

A: In adjacency matrix representation of a graph, the matrix mat[][] of size n*n (where n is the number…

Q: Deterministic PeArmutation (DP) Algorithm Input: a positive integer n. Output: a permutation graph…

A: given data: Input: a positive integer n.Output: a permutation graph G[π] with ∆(G) = n 2 all of its…

Q: Assume you have been given a graph with 1 minimum spanning tree and no repeated edge weights. Using…

A: Boruvka's algorithm is a popular graph algorithm used to find the minimum spanning tree of a given…

Q: Write a java program for dominant set of vertices, graph and at least one adjance vertex of set s.

A: The answer is

Q: Consider an undirected graph with n nodes and m edges. The goal is to find a path between two…

A: To solve this problem, we can use binary search along with Dijkstra's algorithm. The idea is to…

Q: an algorithm to compute the MST of G. Your algorithm should have a runtime of

A: Dear Student, The required algorithm along with explanation is given below -

Q: Given a digraph, find a bitonic shortest path from s to every other vertex (if one exists). A path…

A: The following is the procedure for determining the bitonic shortest path from vertex s to every…

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.