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Unformatted text preview: CS 341: Foundations of Computer Science II Prof. Marvin Nakayama Homework 13 Solutions 1. 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 A = S A such that summationdisplay x A x = summationdisplay x A x. Show that SET-PARTITION is NP-Complete. (Hint: Reduce SUBSET-SUM .) Answer: To show that any problem A is NP-Complete, we need to show four things: (1) there is a non-deterministic polynomial-time algorithm that solves A , (2) any NP-Complete problem B can be reduced to A , (3) the reduction of B to A works in polynomial time, (4) the original problem A has a solution if and only if B has a solution. We now show that SET-PARTITION is NP-Complete. (1) SET-PARTITION NP: Guess the two partitions and verify that the two have equal sums. (2) Reduction of SUBSET-SUM to SET-PARTITION : Recall SUBSET-SUM is defined as follows: Given a set X of integers and a target number t , find a subset Y X such that the members of Y add up to exactly t . Let s be the sum of...
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This note was uploaded on 01/22/2011 for the course CIS 341 taught by Professor Nakayama during the Fall '10 term at NJIT.
- Fall '10