[Solved]-Qn 4 20 Points Consider Set Ai Collection B1 B2 Bm Subsets E Bi C Say Set H C Hitting Set Q37197362

Qn 4 (20 points) Consider a set A = {ai, , an} and a collection B1,B2, Bm of subsets of A (i.e., Bi C A for each i). We say that a set H C A is a hitting set for the collection B1, B2.. … Brn if H contains at least one element from each Bi-that is, if HnB is not empty for eachi so H “hits” all the sets of B). We define the Hitting Set Problem as follows. We are given a set A faan) a collection Bi, B2,…, Bm of subsets of A, and an non-negative integer k. We are asked: is there a hitting set HC A for B, B2,…, Bm so that the size of H is at most k? Prove that the Hitting Set problem is NP-complete. Show transcribed image text Qn 4 (20 points) Consider a set A = {ai, , an} and a collection B1,B2, Bm of subsets of A (i.e., Bi C A for each i). We say that a set H C A is a hitting set for the collection B1, B2.. … Brn if H contains at least one element from each Bi-that is, if HnB is not empty for eachi so H “hits” all the sets of B). We define the Hitting Set Problem as follows. We are given a set A faan) a collection Bi, B2,…, Bm of subsets of A, and an non-negative integer k. We are asked: is there a hitting set HC A for B, B2,…, Bm so that the size of H is at most k? Prove that the Hitting Set problem is NP-complete.

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Answer to Qn 4 (20 points) Consider a set A = {ai, , an} and a collection B1,B2, Bm of subsets of A (i.e., Bi C A for each i). We … . . .