# Complexity Theory Introduction

**Tutor description**

In this appendix, we brieﬂy review the concepts of NP-completeness and reductions. We will use the knapsack problem of Section 3.1 as a running example. Recall that in the knapsack problem, we are given a set of n items I = {1, . . . , n}, where each item i has a value vi and a size si . All sizes and values are positive integers. The knapsack has capacity B, where B is also a positive integer.

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