How to Prove that the 0/1 KNAPSACK problem is NP-Hard. (One way to prove this is to prove the decision version of 0/1 KNAPSACK problem is NP-Complete. In this problem, we use PARTITION problem as the source problem.) (a) Give the decision version of the O/1 KNAPSACK problem, and name it as DK. (b) Show that DK is NP-complete (by reducing PARTITION problem to DK). (c) Explain why showing DK, the decision version of the O/1 KNAPSACK problem, is NP-Complete is good enough to show that the O/1 KNAPSACK problem is NP -hard.
How to Prove that the 0/1 KNAPSACK problem is NP-Hard. (One way to prove this is to prove the decision version of 0/1 KNAPSACK problem is NP-Complete. In this problem, we use PARTITION problem as the source problem.) (a) Give the decision version of the O/1 KNAPSACK problem, and name it as DK. (b) Show that DK is NP-complete (by reducing PARTITION problem to DK). (c) Explain why showing DK, the decision version of the O/1 KNAPSACK problem, is NP-Complete is good enough to show that the O/1 KNAPSACK problem is NP -hard.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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How to Prove that the 0/1 KNAPSACK problem is NP-Hard. (One way to prove this is to
prove the decision version of 0/1 KNAPSACK problem is NP-Complete. In this problem,
we use PARTITION problem as the source problem.)
(a) Give the decision version of the O/1 KNAPSACK problem, and name it as DK.
(b) Show that DK is NP-complete (by reducing PARTITION problem to DK).
(c) Explain why showing DK, the decision version of the O/1 KNAPSACK problem, is
NP-Complete is good enough to show that the O/1 KNAPSACK problem is NP -hard.
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