Answer the questions for the following algorithm. ("weight matrix" is a weighted adjacency matrix with Os on the diagonal) ALGORITHM Floyd(W[1..n, 1.m]) I/Mmplements Floyd's algorithm for the all-pairs shortest-paths problem IInput: The weight matrix W of a graph with no negative-length cycle /Output: The distance matrix of the shortest paths' lengths D+W llis not necessary if W can be overwritten for k-1 to n do for i -1 to n do for j1 to n do D[i. j]- min{D[i. j). D[i. k] + D[k. j]) return D a) What is the input size? b) Are there different best/worst/average cases of different orders of growth? c) Construct a sum describing the number of basic op calls, but do not solve:

Answer the questions for the following algorithm. ("weight matrix" is a weighted adjacency matrix with Os on the diagonal) ALGORITHM Floyd(W[1..n, 1.m]) I/Mmplements Floyd's algorithm for the all-pairs shortest-paths problem IInput: The weight matrix W of a graph with no negative-length cycle /Output: The distance matrix of the shortest paths' lengths D+W llis not necessary if W can be overwritten for k-1 to n do for i -1 to n do for j1 to n do D[i. j]- min{D[i. j). D[i. k] + D[k. j]) return D a) What is the input size? b) Are there different best/worst/average cases of different orders of growth? c) Construct a sum describing the number of basic op calls, but do not solve:

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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Algorithm : (1. Single-destination Shortest Path, 2. Bellman-Ford, 3. Negative-Weight Cycles), Dynamic Programming Define and prove a recurrence for the following problem: Given a directed graph G = (V, E) with edge weight function w : E → R and a source vertex s ∈ V , find a shortest path from s to v for every vertex v ∈ V .
Draw the correct graph..
Please choose the correct answer
Please give me correct solution.
When trying to illustrate a weighted graph, is it possible to run into any problems by utilising adjacency lists?
- Design an exhaustive search algorithm for Vertex Cover and implement the algorithm (either in Java or in Python, whatever is easier for you) - Implement (in the same programming language used for the previous algorithm) the approximate algorithm for Vertex Cover that you find in the material - Carry out some experiments on the running time of the two algorithms with various randomly generated inputs - Compare the solutions given by the approximate algorithm with the solutions of the exhaustive search algorithm, and verify that the results of the former are within the approximation ratio of the results of the latter (the proof of the approximation ratio of the approximation algorithm is in the material)
Proposition Q. ( Generic shortest-paths algorithm) Initialize distTo[s] to 0 andall other distTo[] values to infinity, and proceed as follows: Relax any edge in G, continuing until no edge is eligible. For all vertices w reachable from s, the value of distTo[w] after this computation is the length of a shortest path from s to w (and the value of edgeTo[] is the last edge on that path).
2 в 22 A 6 3 D E 20 9 11 5. G 12 H Figure 4: Directed, weighted graph a) Write an adjacency matrix OR adjacency list to represent the graph in Figure 4. b) Use Dijkstra's algorithm to calculate the single-source shortest paths from vertex A to every other vertex. i Show your steps in the table below. As the algorithm proceeds, cross out old values and write in new ones, from left to right in each cell. If during your algorithm two unvisited vertices have the same distance, use alphabetical order to determine which one is selected first. i. List the vertices in the order in which Dijkstra's algorithm marks them known. 4.
Apply Floyd's algorithm to the following graph. Write Dó matrix as your answer. 2 3 6 4 2. 2. Your answer 4. to 5.
- Minimize the given expression using four variable k-map. F(A, B, C, D) = Em(0, 1, 3, 4, 7, 8, 15). %3D
When trying to show a weighted graph, does the use of adjacency lists provide any problems?
(Generic shortest-paths algorithm) Proposition Q Set distTo[s] to 0 and all other distTo[] values to infinity, then do the following:Continue to relax any edge in G until no edge is eligible.The value of distTo[w] after this calculation is the length of the shortest path from s to w (and the value of edgeTo[] is the final edge on that path) for all vertices w accessible from s.(Generic shortest-paths algorithm) Proposition Q Set distTo[s] to 0 and all other distTo[] values to infinity, then do the following:Continue to relax any edge in G until no edge is eligible.The value of distTo[w] after this calculation is the length of the shortest path from s to w (and the value of edgeTo[] is the final edge on that path) for all vertices w accessible from s.(Generic shortest-paths algorithm) Proposition Q Set distTo[s] to 0 and all other distTo[] values to infinity, then do the following:Continue to relax any edge in G until no edge is eligible.The value of distTo[w] after this calculation is…