Consider the following 3 -PARTITION problem. Given integers a_{... | Filo
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Consider the following 3 -PARTITION problem. Given integers a_{... | Filo
Solution For Consider the following 3 -PARTITION problem. Given integers a_{1}, \ldots, a_{n}, we want to determine whether it is possible to partitio
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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
SOLVED: 10. Consider the following optimization version of the PARTI…
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