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The set-partition problem takes as input a set S of numbers. Th... | Filo

The set-partition problem takes as input a set S of numbers. Th... | Filo

Solution For The set-partition problem takes as input a set S of numbers. The question is whether the numbers can be partitioned into two sets A and \

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SOLVED: 10. Consider the following optimization version of the PARTITION problem. Given a set X of positive integers, our task is to partition X into disjoint subsets A and B such that max{∑ A, ∑ B} is as small as possible. Solving this problem exactly is clearly NP-hard.(a) Prove that the following algorithm yields a (3/2)-approximation.GREEDYPARTITION (X[1 … n]): a ← 0 b ← 0 for i ← 1 to n if a<b a ← a X[i] else b ← b X[i] return max{a, b}(b) Prove that the approximation ratio 3 / 2 cannot be

SOLVED: 10. Consider the following optimization version of the PARTITION problem. Given a set X of positive integers, our task is to partition X into disjoint subsets A and B such that max{∑ A, ∑ B} is as small as possible. Solving this problem exactly is clearly NP-hard.(a) Prove that the following algorithm yields a (3/2)-approximation.GREEDYPARTITION (X[1 … n]): a ← 0 b ← 0 for i ← 1 to n if a<b a ← a X[i] else b ← b X[i] return max{a, b}(b) Prove that the approximation ratio 3 / 2 cannot be

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SOLVED: 10. Consider the following optimization version of the PARTITION problem. Given a set X of positive integers, our task is to partition X into disjoint subsets A and B such that max{∑ A, ∑ B} is as small as possible. Solving this problem exactly is clearly NP-hard.(a) Prove that the following algorithm yields a (3/2)-approximation.GREEDYPARTITION (X[1 … n]): a ← 0 b ← 0 for i ← 1 to n if a<b a ← a X[i] else b ← b X[i] return max{a, b}(b) Prove that the approximation ratio 3 / 2 cannot be

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