Q7:1 Run the Ford-Fulkerson algorithm on the graph assigned to you and determine the maximum flow possible between the source (s) and destination (d) as well as determine the minimum cut of edges (set of edges with the minimum sum of the edge weights) to disconnect the source and destination. Show all the work (including the use of the residual graphs in each iteration).

Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm. (Draw the finished shortest path) b. Use Prim to find the MST (Draw the finished MST) c. Use Kruskal to find the MST (Draw the finished MST) d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.

Run BFS algorithm on the following graph starting with vertex s. Whenever there is a choice of vertices, choose the one that is alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?

1. Run DFS-with-timing on this graph G: give the pre and post number of each vertex. Whenever there is a choice of vertices to explore, always pick the one that is alphabetically first. 2. Draw the meta-graph of G. 3. What is the minimum number of edges you must add to G to make it strongly connected (i.e., it consists of a single connected component after adding these edges)? Give such a set of edges. b.

3. Kleinberg, Jon. Algorithm Design (p. 519, q. 28) Consider this version of the Independent Set Problem. You are given an undirected graph G and an integer k. We will call a set of nodes I "strongly independent" if, for any two nodes v, u € I, the edge (v, u) is not present in G, and neither is there a path of two edges from u to v. That is, there is no node w such that both (v, w) and (u, w) are present. The Strongly Independent Set problem is to decide whether G has a strongly independent set of size at least k.   Show that the Strongly Independent Set Problem is NP-Complete.

Hello, i have this Dijkstra’s exercise. could you help me to solve it?

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 vį 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 €₁,7 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.

I have a directed graph with N nodes.  How can I tell if the graph has a cycle?   Your answer should be an algorithm in English.  It is nice but not essential for you to give the name of the algorithm. You should describe how the algorithm works.

Mark Zuckerberg, the CEO of Facebook, has hired you to lead the Facebook Algorithms Group. He has asked you to use various graph algorithms to analyze the world's largest social network. The Facebook Graph has 2.8 billion vertices, with each vertex being a Facebook user. Two vertices are connected provided those two users are "friends". The first decision you need to make is how you want to model the Facebook graph. Determine whether you should use an adjacency-list representation or an adjacency-matrix representation.

plese modify the code according to the instruction in c programming  Please Modify this code according to this instructions   cmds.c   – Need to modify the Cmd struct to include:   “ms” and “h”   – Add code in mem_display(), help(), mem_set() functions   – Command routine calls with 2 arguments, e.g.   mem_display(Cmd *cp, char *arguments)   &cmds[0]   Address of the string “10000”   – If we enter a command “md 10000” to display the contents of 16 locations starting with 10000, the arguments passed are:       file:     cmds.c   /* the Makefile arranges that #include <..> searches in the right    places for these headers-- 200920*/   #include <stdio.h> #include "slex.h" /*===================================================================* * *   Command table for tutor program -- an array of structures of type *   cmd -- for each command provide the token, the function to call when *   that token is found, and the help message. * *   slex.h contains the typdef for…