In the maximum coverage problem, we have a set of n elements E, a set of m sets (which are subsets of E), S1, S2, .., Sm. We are also given an integer m ≥ k ≥ 1. Our goal is to pick k sets that cover the maximum number of elements. We say an element is covered if we pick at least one set from S1, S2, .., Sm in our solution that contains that element. Devise a greedy algorithm that is a (1 −1/e) approximation. That is if there is an optimum solution that can cover OPT number of elements, the greedy algorithm is guaranteed to cover at least  (1 −1/e) *OPT elements. Here e is the base of natural logarithm. Use the following relation (1-1/k)k ~1/e.

Q: Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Select the collection of sets that forms a partition of A. O…

A: The collection of sets that forms a partition of A must satisfy the following properties: The sets…

Q: If we choose to represent each genotype as a partial permutation, then provide an algebraic…

A: genotype as a partial permutation, then provide an algebraic expression, in terms of n, for the size…

Q: Given an array of numbers X₁ = {x₁, x2, ..., n } an exchanged pair in X is a pair xi, xj such that i…

A: The objective of the question is to design a divide-and-conquer algorithm that counts the number of…

Q: For σarthm := (0, S, +, ·). Prove PA ⊨ ∀x (x ≠ 0 ⟹ ∃y(x = S(y))). In English, this say that every…

A: Given statement PA ⊨ ∀x (x ≠ 0 ⟹ ∃y(x = S(y)))

Q: For any given AVL tree T of n elements, we need to design an algorithm that finds elements x in T…

A: B) O(mlogn)

Q: Let A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6, 7} and C = {a, b, c, d, e} 17. Give an example of…

A: Refer below the example for above asked question:

Q: A bus driver has a job to show a group of tourists around different cities. All edges denote the…

A: Answer: The best route to take is 1 - 2 - 4 - 7 when 1 is the departure city and 7 is the…

Q: Given a string ₁... we wish to find the length of its longest increasing subsequence, that is, the…

A: Your answer is given below.

Q: Problem 28. Prove that, for every IL FSC C = (Q,δ,ν,s) and every n ∈ N, there is an input string w ∈…

A: This proof is based on the theory of Information Lossless Finite-State Channel (IL FSC). An IL FSC…

Q: For the one-dimensional version of the closest-pair problem, i.e., for the problem of finding two…

A: According to the information given:- We have to design and determine divide-and-conquer technique,…

Q: Problem 3: In this problem we assume that elements are drawn from a universal set U. (i) We insert n…

A: A 'Universal Set' is a set containing all of the components under examination in any given context…

Q: Consider a list of n positive integers a1, a2, ..., an. Given a query positive integer m, we are…

A: In this question we have been asked to find the most efficient way to search a list for a given…

Q: • or if Zi > Zi+1 it must be th

A: Graded question

Q: Create an algorithm for the monotonic evaluation function, algorithm A*. Graph G = (V, E); start…

A: given data: Graph G = (V, E); start vertex s; target vertex r; A-Star(G, s, r) in; out: maps as: V…

Q: Let G = (V,E) be a bipartite graph, but this time it is a weighted graph. The weight of a complete…

A:

Q: Algorithm for minimising a partition given a pair of points Input: a group G formed by S = s 1,…

A: Algorithm for minimising a partition given a pair of points:

Q: Provide a tight asymptotic upper bound on E[ H] by following the steps below. (a) Show that P[H > m]…

A: According to the question, we have to provide a tight asymptotic upper bound on E[H] by following…

Q: What is the worst-case running-time of the isGraphConnected function below which tests whether a…

A: Ans:   e.  O(n+m)