### Dijkstra's Algorithm and Negative Cost EdgesDijkstra's algorithm for computing lowest cost paths from a single source node is always correct for graphs without negative-cost edges. If a graph has negative-cost edges, the algorithm might or might not give the right answer. For the directed weighted graph below, list all nodes which Dijkstra's algorithm produces the wrong path and write the correct lowest-cost path.#### Graph DescriptionIn the graph provided:- Node A has two directed edges: - To node B with a weight of 7. - To node C with a weight of 3. - Node B has a directed edge: - To node D with a weight of -2. - Node C has a directed edge: - To node D with a weight of 3. - Node D has a directed edge: - To node E with a weight of -1.#### Analysis Questions1. The correct lowest-cost path from A to E should be: *Answer hidden* 2. The lowest-cost path from A to E that is produced from Dijkstra's algorithm (*Answer hidden*):*Note: The answers are intentionally hidden for educational purposes in this transcription to encourage problem-solving.*

Dijkstra's algorithm for computing lowest cost paths from a single source node is always correct for graphs without negative-cost edges. If a graph has negative-cost edges, the algorithm might or might not give the right answer. For the directed weighted graph below, list all nodes which Dijkstra's algorithm produces the wrong path and write the correct lowest-cost path. -2 7 -1 A B.

Dijkstra's algorithm for computing lowest cost paths from a single source node is always correct for graphs without negative-cost edges. If a graph has negative-cost edges, the algorithm might or might not give the right answer. For the directed weighted graph below, list all nodes which Dijkstra's algorithm produces the wrong path and write the correct lowest-cost path. -2 7 -1 A B.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Let G be a graph, where each edge has a weight. A spanning tree is a set of edges that connects all the vertices together, so that there exists a path between any pair of vertices in the graph. A minimum-weight spanning tree is a spanning tree whose sum of edge weights is as small as possible. Last week we saw how Kruskal's Algorithm can be applied to any graph to generate a minimum-weight spanning tree. In this question, you will apply Prim's Algorithm on the graph below. You must start with vertex A. H 4 4 1 3 J 2 C 10 4 8 B 9 F 18 8 There are nine edges in the spanning tree produced by Prim's Algorithm, including AB, BC, and IJ. Determine the exact order in which these nine edges are added to form the minimum-weight spanning tree. 3.
We know that if the heuristic function in A* is good enough, then A* can always find a shortest weighted path between two vertices, and is generally much faster than Dijkstra. Assume we are using a graph where a good heuristic function is well defined for A*, such that A* can always find the same shortest paths as Dijkstra. Briefly explain when you should choose Dijkstra over A* in this case.
17 B 5 3 7 6 18 14 15 12 2 8 10 1 16 11 13 J 9 I 15 H a. Consider the graph given above. Use Prim's and Kruskal's algorithm to find the minimum spanning tree. b. What is the total weight of the spanning trees? List the weights of the selected edges separated by commas in the order of selection.
Algebraic Preis’ AlgorithmAlgorithm due to Preis provides a different way to solve the maximal weightedmatching problem in a weighted graph. The algorithm consists of the followingsteps.1. Input: A weighted graph G = (V, E, w)2. Output: A maximal weighted matching M of G3. M ← Ø4. E ← E5. V ← V6. while E = Ø7. select at random any v ∈ V8. let e ∈ E be the heaviest edge incident to v9. M ← M ∪ e10. V ← V {v}11. E ← E \ {e and all adjacent edges to e}show two ways of implementing this algorithm in Python
Algebraic Preis’ AlgorithmAlgorithm due to Preis provides a different way to solve the maximal weightedmatching problem in a weighted graph. The algorithm consists of the followingsteps.1. Input: A weighted graph G = (V, E, w)2. Output: A maximal weighted matching M of G3. M ← Ø4. E ← E5. V ← V6. while E = Ø7. select at random any v ∈ V8. let e ∈ E be the heaviest edge incident to v9. M ← M ∪ e10. V ← V {v}11. E ← E \ {e and all adjacent edges to e} show two ways of implementing this algorithm in Python
Given N cities represented as vertices V₁, V2,..., UN on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices v; and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). Assume that all edges have different values, and e₁, has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.
With a given graph below, run the Bellman-Ford Algorithm to find the shortest path from node s to all nodes. For example, (0, 100, 23, 300, 50) for (node 1, node 2, node 3, node 4, node 5)
A weighted, directed graph is a suitable representation to represent the daily airline routes flown by a small airline. The airline have the following daily flights: - Three flights from Cape Town to Johannesburg, - Two flights from Johannesburg to Cape Town. - Four flights from Johannesburg to Durban. - Three flights from Durban to Johannesburg. - One flight from Johannesburg to George. - One flight from George to Johannesburg. Draw a graph that represents this problem
Apply the Bellman-Ford algorithm to find the shortest path from node A to all the other nodes in the graph below. Write down every step in the algorithm. A 2 to 2 3
We recollect that Kruskal's Algorithm is used to find the minimum spanning tree in a weighted graph. Given a weighted undirected graph G = (V , E, W), with n vertices/nodes, the algorithm will first sort the edges in E according to their weights. It will then select (n-1) edges with smallest weights that do not form a cycle. (A cycle in a graph is a path along the edges of a graph that starts at a node and ends at the same node after visiting at least one other node and not traversing any of the edges more than once.) Use Kruskal's Algorithm to nd the weight of the minimum spanning tree for the following graph.
My id last two digit : 21