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1- Let G = ( V , E ) be an undirected graph and let R be a relation on V defined by vRw if and only if there exists a path from v to w . (Recall there is a path of length zero from any vertex to itself.)1. Show that R is an equivalence relation.2. What are the equivalence classes of this relation?3. Show that the reachability matrix R for an undirected graph with n vertices can be constructed in 0 ( n 2 )time.
2- compute the transitive closure of the relation A given in Example 9.1. Show the matrix after each pass of the outermost for loop.
Transitive closure of one relationFor the following A,the transitive closure is R.
Warshall's Algorithminput: A and n, where A is an n X n adjacency matrix output: R, the n X n transitive closure matrix of A voidtranstivieClosure(boolean[][] A, int n, boolean [][] R) inti, j, k; Copy A into R; Set all main diagonal entries, r[i][i] to true; for (k=1; k<=n; k++) for (i=1; i<=n; i++) for (j=1; j<=n; j++)r[i][j] = r[i][j] | (r[i][k] & r[k][j]);
Every big organization has large documents or databases containing data used in operating the business. Does a data warehouse differ from these operational files or databases?
Illustrate how to use depth-first search to find out in time O(|E|+|V |) whether undirected graph is 2-colorable. Describe and explain your strategy.
Write a recursive implementation of Euclid's algorithm for finding the greatest common divisor (GCD) of two integers
Study feasibility analysis for jobs of LRT algorithm when preemption is allowed. Which scheduling algorithm is best suited for high speed networks and why? Distinguish between static and dynamic systems.
Data from the Astronaut.data must be read into a 1-D array of structures(or classes) named ASTRONAUT and thereafter all processing must be performed on the array of structures.
The node's right child. If the nil pointer is represented by 00 and the tree's root pointer contains 53, how many terminal nodes are in tree?
Create an applet document that prompts the user for an ID number and an age. Construct an Exception class and throw an Exception of that class if the ID is not in the range of valid ID numbers.
Many of your family members have discovered that you are using Excel to organize the information for the high school reunion. Your Uncle Larry wants to make an inventory of the over 800 video games that he collects.
Develop the pseudo code needed to find the average of ten 8-bit numbers. Use a loop.
For a message, he computes the hash value H = (VChar 1 x VChar 2 x VChar 3 ...x VChar N) mod(26).
Assume Alice wishes to send an e-mail to Bob. Bob has a public private key pair, Alice has Bob's certificate. But Alice does not have a public, private key pair.
A brief introduction of the sorting algorithm that you have selected and how the two versions of the algorithm compare.
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