Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:
The Bellman-Ford algorithm makes |V|-1 = 7-1 = 6 passes through the edge list E. Each pass relaxes the edges in the order they appear in the edge list. As with Dijkstra's algorithm, we record the current best known cost D[V] to reach each vertex V from the start vertex S. Initially D[A]=0 and D[V]=+oo for all the other vertices V # A. Run Bellman-Ford on the given graph, starting at vertex A, and using the order of set E above, show me the contents of array DO after each iteration (6 arrays in all.)
Homework Answers
The above image shows all the
iterations and the respective distance of all the nodes.
For better results you should always arrange the edges in order of their position from the source node.
In case of any further queries, please do let us know.
Thanks
Add Answer to:
Consider the following weighted, directed graph G. There are 7 vertices and 10 edges. The edge list E is as follows:
5. (10 pts) Give a concrete example of a directed and weighted graph G and two...
5. (10 pts) Give a concrete example of a directed and weighted graph G and two vertices u and v, where the Dijkstra's algorithm does not find the shortest path from u to v in G but the Bellman-Ford algorithm does. Obviously such a graph must have at least one negative- weight edge.
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac,...
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac, af ca. bc. be.bf. cd, ce, de, df). Weights: w(ab) = 2 w(ac) = 5, w(af) = 10, w(ca) = 2. w(be) = 2. w(be) = 10, w(bf) = 11. w(cd)= 9. w(ce) = 7. w(de) = 2. w(df) = 2. a. Draw the Graph. This is a directed, weighted graph so you need to include arrows and weights. You can insert a pic...
3. The indegree of a vertex u is the number of incoming edges into u, .e, edges of the form (v,u)...
3. The indegree of a vertex u is the number of incoming edges into u, .e, edges of the form (v,u) for some vertex v Consider the following algorithm that takes the adjacency list Alvi, v2, n] of a directed graph G as input and outputs an array containing all indegrees. An adjacency list Alvi, v.. /n] is an array indexed by the vertices in the graph. Each entry Alv, contains the list of neighbors of v) procedure Indegree(Alvi, v2,......
Let G (V, E) be a directed graph with n vertices and m edges. It is known that in dfsTrace of G t...
Let G (V, E) be a directed graph with n vertices and m edges. It is known that in dfsTrace of G the function dfs is called n times, once for each vertex It is also seen that dfs contains a loop whose body gets executed while visiting v once for each vertex w adjacent to v; that is the body gets executed once for each edge (v, w). In the worst case there are n adjacent vertices. What do...
Consider a directed acyclic graph G = (V, E) without edge lengths and a start vertex...
Consider a directed acyclic graph G = (V, E) without edge lengths and a start vertex s E V. (Recall, the length of a path in an graph without edge lengths is given by the number of edges on that path). Someone claims that the following greedy algorithm will always find longest path in the graph G starting from s. path = [8] Ucurrent = s topologically sort the vertices V of G. forall v EV in topological order do...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in the order they were added to the minimum spanning tree. Demonstrate Dijkstra's algorithm on the graph, using vertex A as the source. Write the vertices in the order which they are marked and compute all distances at each step.
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 _______ .
5. The in-degree of a vertex in a directed graph is the number of edges directed...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
Run Dijkstra's algorithm on the graph G below, where s is the source vertex.
Run Dijkstra's algorithm on the graph G below, where s is the source vertex. Draw a table that shows the vertices in Q at each iteration. Write thed and I values of each vertex. Color the edges in the shortest-path tree, similar to the example from the notes. List the order in which vertices are added to S. Use the algorithm learned in class.
Give an example of a graph G with at least 10 vertices such that the greedy...
Give an example of a graph G with at least 10
vertices such that the greedy 2-approximation algorithm for
Vertex-Cover given below is guaranteed to produce a suboptimal
vertex cover.
Algorithm Vertex CoverApprox(G): Input: A graph G Output: A small vertex cover C for G while G still has edges do select an edge e (v, w) of G add vertices v and w to C for each edge f incident to v or w do remove f from G...
5. (10 pts) Give a concrete example of a directed and weighted graph G and two vertices u and v, where the Dijkstra's algorithm does not find the shortest path from u to v in G but the Bellman-Ford algorithm does. Obviously such a graph must have at least one negative- weight edge.
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac, af ca. bc. be.bf. cd, ce, de, df). Weights: w(ab) = 2 w(ac) = 5, w(af) = 10, w(ca) = 2. w(be) = 2. w(be) = 10, w(bf) = 11. w(cd)= 9. w(ce) = 7. w(de) = 2. w(df) = 2. a. Draw the Graph. This is a directed, weighted graph so you need to include arrows and weights. You can insert a pic...
3. The indegree of a vertex u is the number of incoming edges into u, .e, edges of the form (v,u) for some vertex v Consider the following algorithm that takes the adjacency list Alvi, v2, n] of a directed graph G as input and outputs an array containing all indegrees. An adjacency list Alvi, v.. /n] is an array indexed by the vertices in the graph. Each entry Alv, contains the list of neighbors of v) procedure Indegree(Alvi, v2,......
Let G (V, E) be a directed graph with n vertices and m edges. It is known that in dfsTrace of G the function dfs is called n times, once for each vertex It is also seen that dfs contains a loop whose body gets executed while visiting v once for each vertex w adjacent to v; that is the body gets executed once for each edge (v, w). In the worst case there are n adjacent vertices. What do...
Consider a directed acyclic graph G = (V, E) without edge lengths and a start vertex s E V. (Recall, the length of a path in an graph without edge lengths is given by the number of edges on that path). Someone claims that the following greedy algorithm will always find longest path in the graph G starting from s. path = [8] Ucurrent = s topologically sort the vertices V of G. forall v EV in topological order do...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in the order they were added to the minimum spanning tree. Demonstrate Dijkstra's algorithm on the graph, using vertex A as the source. Write the vertices in the order which they are marked and compute all distances at each step.
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
Give an example of a graph G with at least 10
vertices such that the greedy 2-approximation algorithm for
Vertex-Cover given below is guaranteed to produce a suboptimal
vertex cover.
Algorithm Vertex CoverApprox(G): Input: A graph G Output: A small vertex cover C for G while G still has edges do select an edge e (v, w) of G add vertices v and w to C for each edge f incident to v or w do remove f from G...
Most questions answered within 3 hours.
-
Suppose in the short run a firm’s production function is given
by Q = L1/2*K1/2, and...
asked 58 seconds ago -
Calculation of number of protons, neutrons , and electrons
If given the mass # of 74...
asked 2 minutes ago -
On the Apollo 14 mission to the moon, astronaut Alan Shepard hit
a golf ball with...
asked 14 minutes ago -
are primates eutherians?
i know eutherians come from therians but does primates come from
eutharia bc...
asked 19 minutes ago -
Calculate the specific heat of a certain unknown metal, if it
requires 195 joules of heat...
asked 30 minutes ago -
Identify the characteristics of a successful
project.
Describe the phases the project lifecycle.
Define the roles...
asked 39 minutes ago -
1. In Module 2 "headers" and "footers" are
described. Explain the difference between them and how...
asked 34 minutes ago -
Three polarizing filters are stacked with the polarizing axes of
the second and third at 58.5...
asked 43 minutes ago -
The capacitance in a series RCL circuit is C1 = 3.3 μF, and
the corresponding resonant...
asked 53 minutes ago -
A 357.7-gram sample of an unknown substance (MM = 92.41 g/mol)
is heated from -23.1 °C...
asked 52 minutes ago -
The project aims to design a network for a casino. The casino
has 10 floors including...
asked 57 minutes ago -
Combustion of an unknown compound containing only carbon and
hydrogen produces 54.9 g of CO₂ and...
asked 1 hour ago