Question: In the HITTING-SET problem, we are given a set U of items, and a collection of subsets of U, S1, S2,...,Sm. The problem is to

In the HITTING-SET problem, we are given a set U of items, and a collection of subsets of U, S1, S2,...,Sm. The problem is to find a smallest subset T of U such that T “hits” every subset Si, that is, T ∩ Si = ∅, for i = 1,...,m. Design a polynomial-time O(log n)-approximation algorithm for HITTING-SET.

Step by Step Solution

★★★★★

3.34 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Polynomial Time Approximation Scheme PTAS is a type of approximate algorithms tha... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Data Structures Algorithms Questions!

Consider a single machine scheduling problem, where we are given a set, T, of tasks specified by their start times and finish times, as in the task scheduling problem, except now we have only one...

We are given a directed graph G = (V, E) on which each edge (u, v) E has an associated value r(u, v), which is a real number in the range 0 r(u, v) 1 that represents the reliability of a...

Suppose we are given a set of telescope observation requests, specified by triples of (s i , f i , b i ), defining the start times, finish times, and benefits of each observation request as L = {(1,...

The Set Cover problem is defined thus: Given a universal set U and a set of subsets s-: {si, S2, . . . , Sm} of? find the smallest number of subsets such that their union equals U. For example U=...

Algorithm question The Set Packing Problem is stated as follows: Given a set U of n elements, a collection S_1, S_2, ellipsis, S_m of subsets of U, and a number k, does there exist a collection of at...

Recall the following definition of the minimum Set Cover problem: Given a set U of elements and a collection S1, . . . , Sm of subsets of U, what is the smallest collection of these sets whose union...

Data Structure and Algorithms || EX01: Due to 17th of Feb at 11:59 PM. 1- Several possible algorithms might come to mind to solve this problem. Perhaps the most popular idea is the nearest-neighbor...

1- Several possible algorithms might come to mind to solve this problem. Perhaps the most popular idea is the nearest-neighbor heuristic algorithm is used to solve the shortest tour problem. Starting...

need typed answer do anyone your wish dont provide code need algorithm 2. A dominating set of a graph is a subset D of vertices such that every vertex that is not in D is adjacent to some vertex in...

Question 1 : Consider the Differentiated Set Coverage Problem: Input: n items, U = 1 , 2 , . . . , n , coverage requirements of the items f = f 1 , f 2 , . . . , fn , m sets, S 1 , S 2 , . . . , Sm ,...

The academic office at the Hogwarts School of Witchcraft and Wizardry has compiled data about students' grades. The data is provided as text from standard input in three parts: information about...

Solve Exercise 10.11 using the UNIFAC method for Kvalues and obtain the converged solution.

Chapter 4 Problem 1: The cost of tuition increases each year by a geometric gradient of 10%. Calculate the PV, FV, and AV (PMT) of tuition costs. In year one, the tuition cost is $10,000, increasing...

4. Teresa is a civil engineer who uses her automobile for business. Teresa drove her automobile a total of 22,650 miles during 2010, of which 95 percent was business mileage. The actual cost of...

Show that the sum which appears in the analysis of heap-sort, is ?(n log n). log i, 1og , i=1

Give a concrete implementation of the pop method in the context of the MutableMapping class, relying only on the five primary abstract methods of that class.

Give a concrete implementation of the items( ) method in the context of the MutableMapping class, relying only on the five primary abstract methods of that class. What would its running time be if...

Bird's Eye Treehouses, Incorporated, a Kentucky company, has determined that a majority of its customers are located in the Pennsylvania area. It therefore is considering using a lockbox system...

Scenario: A therapist wanted to examine marital happiness in couples participating in therapy at her clinic. Couples were randomly assigned to participate in individual, couples, or group therapy....

If sales volume decreases, and all other factors remain unchanged, the contribution margin ratio will decrease - Vf. 1. 2. In two companies making the same product and with the same total sales and...