Write A greedy algorithm to find the maximal independent sets for matroids step by step.
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Write A greedy
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- 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.Use the Transform-and-Conquer algorithm design technique with Instance Simplification variant to design an O(nlogn) algorithm for the problem below. Show the pseudocode. Given a set S of n integers and another integer x, determine whether or not there exist two elements in S whose sum is exactly x.Please Answer this in Python language: You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each vertex i, a number C; such that 1 ≤ C; ≤ N and Vi‡j, C; ‡ Cj. For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁. You want to minimise maai[1..N) Di - mini[1..N) Di. Output the minimum possible value of this expression for a valid assignment as described above, and also print the corresponding assignment. Note: The given graph need not be connected. • If there are multiple possible assignments, output anyone. • Since the input is large, prefer using fast input-output methods. Input 1 57 12 13 14 23 24 25 35 Output 2 43251 Q
- Analyze the approximation algorithm of the problem consists of a finite set X and a family F of subsets of X, such that every element of X belongs to at least one subset.3. Given the following minterm expansion: F(a, b, c, d) = Em(0, 2, 3, 4, 8, 10, 11, 15) Draw the K-Map Find out all essential prime implicants, do it systematically. Do you need additional loops to cover all the minterms. If yes, find the additional prime implicants. Get the minimum SO.The Triangle Vertex Deletion problem is defined as follows: Given: an undirected graph G = (V, E) , with IVI=n, and an integer k>= 0. Is there a set of at most k vertices in G whose deletion results in deleting all triangles in G? (a) Give a simple recursive backtracking algorithm that runs in O(3^k * ( p(n))) where p(n) is a low-degree polynomial corresponding to the time needed to determine whether a certain vertex belongs to a triangle in G. (b) Selecting a vertex that belong to two different triangles can result in a better algorithm. Using this idea, provide an improved algorithm whose running time is O((2.562^n) * p(n)) where 2.652 is the positive root of the equation x^2=x+4
- Is the following statement true or false? a. Performing one rotation always preserves the AVL property. b. For any two functions f and g, we always have either f = O(g) or g = O(f). c. We run the breadth-first search algorithm (BFS) on a undirected graph G such that all edges have the same weight. BFS returns the shortest path from a source vertex s to any other vertex.Apply the Breadth first traversal algorithm to the undirected graph G given in Example and replicated here for convenience. The goal is to do a Breadth first search for the key 9.adgis s o (6): = min { d(v) Ive V3 is the minimum degree of G. 0612 Z9Nto JJ V PO Go is called K-connected if IGI>K and GIX is connected for every set x CV with 1X1For the one-dimensional version of the closest-pair problem, i.e., for the problem of finding two closest numbers among a given set of n real num- bers, design an algorithm that is directly based on the divide-and-conquer technique and determine its efficiency class. Is it a good algorithm for this problem?Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x e X and y e Y and (y – {x) is divisible by 6Consider a graph and implement Breadth-first search, Uniform-cost search, Depth-first search, Depth-limited search, Iterative deepening depth-first search and Bidirectional search using your favorite programming language. Also draw and visualize the solution.SEE MORE QUESTIONS