Question 1

Figure from the passage in the original paper Based on the above data answer the given subquestions. Figure from the original question paper Figure from the passage in the original paper Based on the above data answer the given subquestions. Consider the following reduction from 3-PARTITION to 2-PARTITION: let $\{a_1, \ldots, a_{3n}\}$ be the instance of 3-PARTITION where $\sum_{i=1}^{3n} a_i = nT$. Now consider the instance of 2-PARTITION made of the numbers: $$\{a_1, T - a_1, a_2, T - a_2, \ldots, a_n, T - a_n\},$$ i.e, the reduced instance consists of the first $n$ numbers of the original problem, and $n$ new numbers formed by taking the difference between each of the input numbers and the common sum $T$. This reduction: Figure from the passage in the original paper Based on the above data answer the given subquestions. Consider the following reduction from 3-PARTITION to 2-PARTITION: let $\{a_1, \ldots, a_{3n}\}$ be the instance of 3-PARTITION where $\sum_{i-1}^{3n} a_i = nT$. Now consider the instance of 2-PARTITION made of the numbers: $$\{a_1, a_2, \ldots, a_{2n}\},$$ i.e, the reduced instance simply consists of the first $2n$ numbers of the 3-PARTITION instance. This reduction: