Consider the width search algorithm from a start node s. The diameter of an undirected, contiguous...
Consider the width search algorithm from a start node s. The diameter of an undirected, contiguous Graph G = (V, E) is defined as the maximum over all node pairs v, w ∈ V of the length of the shortest path from v to w. We assume that each edge has the length of 1.
Specify an extension of the width search algorithm in pseudo
code that has the diameter of an undirected graph G = (V, E). First
explain briefly the idea of your algorithm. Determine the runtime
of the algorithm and give reasons, why it's correct.
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Consider the width search algorithm from a start node s. The
diameter of an undirected, contiguous...
Let G = (V, E, w) be a connected weighted undirected graph. Given a vertex s...
Let G = (V, E, w) be a connected weighted undirected graph. Given a vertex s ∈ V and a shortest path tree Ts with respect to the source s, design a linear time algorithm for checking whether the shortest path tree Ts is correct or not.(C pseudo)
3. (15 pts) The diameter of a graph is the largest of all shortest-path distances in the graph. I...
3. (15 pts) The diameter of a graph is the largest of all shortest-path distances in the graph. In other words, if So(x, y) is the length of the shortest path from| x to y in graph G = (V,E), then the diameter of G is max (Sc(t,y)J Give an algorithm to compute the diameter of an undirected graph G (V. E), with running time at lnost O (V12 + VİİE). Include an analysis of the running time.
3. (15...
Q1: Here we consider finding the length of the shortest path between all pairs of nodes...
Q1: Here we consider finding the length of the shortest path between all pairs of nodes in an undirected, weighted graph G. For simplicity, assume that the n nodes are labeled 1; 2; : : : ; n, that the weight wij of any edge e = (i; j) is positive and that there is an edge between every pair of nodes. In this question, the goal is to solve this via dynamic programming. Note that the algorithm you will...
2) Let G ME) be an undirected Graph. A node cover of G is a subset...
2) Let G ME) be an undirected Graph. A node cover of G is a subset U of the vertex set V such that every edge in E is incident to at least one vertex in U. A minimum node cover MNC) is one with the lowest number of vertices. For example {1,3,5,6is a node cover for the following graph, but 2,3,5} is a min node cover Consider the following Greedy algorithm for this problem: Algorithm NodeCover (V,E) Uempty While...
please answer one of the two 1. (25) [Single-source shortest-path: algorithm tracing] Show the tracing of...
please answer one of the two
1. (25) [Single-source shortest-path: algorithm tracing] Show the tracing of Dijkstra's shortest path search algorithm on the weighted directed graph shown below. Do the tracing it twice, first starting with the nodes and, second, starting with the node z. For each tracing, each time the shortest path to a new node is determined, show the graph with the shortest path to the node clearly marked and show inside the node the shortest distance to...
Consider the problem of finding the shortest paths in a weighted directed graph using Dijkstra's algorithm.
Consider the problem of finding the shortest paths in a weighted directed graph using Dijkstra's algorithm. Denote the set of vertices as V, the number of vertices as |V|, the set of edges as E, and the number of edges as |E|. Answer the following questions.Below is a pseudo-code of the algorithm that computes the length c[v] of the shortest path from the start node s to each node v. Answer code to fill in the blank _______ .
2 Node removal Consider the following specifications: Algorithm 1 Removes node vk from graph G represented...
2 Node removal Consider the following specifications: Algorithm 1 Removes node vk from graph G represented as an adjacency matrix A Require: A E {0,1}"x", kEN, k<n Ensure: A' E {0,1)(n-1)×(1-1) 1: function NODEREMOVAL(A,k) 2: ... 3: return A 4: end function The function accepts an adjacency matrix A, which represents a graph G, and an integer k, and returns adjacency matrix A', representing graph G', that is the result of removing node the k-th node us from G. Question:...
please help Programming: Undirected Graphs 10. Run the BFS algorithm on this graph to compute the shortest paths between 0 and every other node. For reference, the BFS algorithm is shown on the next...
please help
Programming: Undirected Graphs 10. Run the BFS algorithm on this graph to compute the shortest paths between 0 and every other node. For reference, the BFS algorithm is shown on the next page. Use the adjacency list above for the order of the nodes explored and follow the trace format shown before. Your answer must include the values of v, queue, and edge To, as they update. [20 point s 0 3, 1 10, 4, 3, 2 21.5...
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the gr...
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the graph is the set of all nodes that are adjacent (or directly connected) to v. Subsequently, we can define the neighbourhood degree of the node v as the sum of the degrees of all its neighbours (those nodes that are directly connects to v) (a) Design an algorithm that returns a list containing the neighbourhood degree for each node v V,...
Input a simple undirected weighted graph G with non-negative edge weights (represented by w), and a...
Input a simple undirected weighted graph G with non-negative edge weights (represented by w), and a source node v of G. Output: TDB. D: a vector indexed by the vertices of G. Q: priority queue containing the vertices of G using D[] as key D[v]=0; for (all vertex ut-v) [D[u]-infinity:) while not Q. empty() 11 Q is not empty fu - Q.removein(); // retrieve a vertex of Q with min D value for (all vertex : adjacent to u such...
3. (15 pts) The diameter of a graph is the largest of all shortest-path distances in the graph. In other words, if So(x, y) is the length of the shortest path from| x to y in graph G = (V,E), then the diameter of G is max (Sc(t,y)J Give an algorithm to compute the diameter of an undirected graph G (V. E), with running time at lnost O (V12 + VİİE). Include an analysis of the running time.
3. (15...
2) Let G ME) be an undirected Graph. A node cover of G is a subset U of the vertex set V such that every edge in E is incident to at least one vertex in U. A minimum node cover MNC) is one with the lowest number of vertices. For example {1,3,5,6is a node cover for the following graph, but 2,3,5} is a min node cover Consider the following Greedy algorithm for this problem: Algorithm NodeCover (V,E) Uempty While...
please answer one of the two
1. (25) [Single-source shortest-path: algorithm tracing] Show the tracing of Dijkstra's shortest path search algorithm on the weighted directed graph shown below. Do the tracing it twice, first starting with the nodes and, second, starting with the node z. For each tracing, each time the shortest path to a new node is determined, show the graph with the shortest path to the node clearly marked and show inside the node the shortest distance to...
2 Node removal Consider the following specifications: Algorithm 1 Removes node vk from graph G represented as an adjacency matrix A Require: A E {0,1}"x", kEN, k<n Ensure: A' E {0,1)(n-1)×(1-1) 1: function NODEREMOVAL(A,k) 2: ... 3: return A 4: end function The function accepts an adjacency matrix A, which represents a graph G, and an integer k, and returns adjacency matrix A', representing graph G', that is the result of removing node the k-th node us from G. Question:...
please help
Programming: Undirected Graphs 10. Run the BFS algorithm on this graph to compute the shortest paths between 0 and every other node. For reference, the BFS algorithm is shown on the next page. Use the adjacency list above for the order of the nodes explored and follow the trace format shown before. Your answer must include the values of v, queue, and edge To, as they update. [20 point s 0 3, 1 10, 4, 3, 2 21.5...
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the graph is the set of all nodes that are adjacent (or directly connected) to v. Subsequently, we can define the neighbourhood degree of the node v as the sum of the degrees of all its neighbours (those nodes that are directly connects to v) (a) Design an algorithm that returns a list containing the neighbourhood degree for each node v V,...
Input a simple undirected weighted graph G with non-negative edge weights (represented by w), and a source node v of G. Output: TDB. D: a vector indexed by the vertices of G. Q: priority queue containing the vertices of G using D[] as key D[v]=0; for (all vertex ut-v) [D[u]-infinity:) while not Q. empty() 11 Q is not empty fu - Q.removein(); // retrieve a vertex of Q with min D value for (all vertex : adjacent to u such...
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