Consider the Knapsack problem. Let I be the set of items, a, b, be the size...
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Consider the Knapsack problem. Let I be the set of items, a, b, be the size and the profit of item i for any i I, and W be the knapsack size. Consider the following greedy algorithm: 1. Sort the items in I in non-increasing order of b;/a, for all i € I. 2. Pack the items in the knapsack whenever possible according to the above order. Show that the above algorithm can perform arbitrarily bad, i.e., for any fixed constant € > 0, there exists an instance such that the approximation ratio of the above algorithm on this instance is at most €. Consider the Knapsack problem. Let I be the set of items, a, b, be the size and the profit of item i for any i I, and W be the knapsack size. Consider the following greedy algorithm: 1. Sort the items in I in non-increasing order of b;/a, for all i € I. 2. Pack the items in the knapsack whenever possible according to the above order. Show that the above algorithm can perform arbitrarily bad, i.e., for any fixed constant € > 0, there exists an instance such that the approximation ratio of the above algorithm on this instance is at most €.
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The Knapsack problem is a wellknown NPhard optimization problem To show that the given greedy algori... View the full answer
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
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