Algorithms Analysis Practice Test

The statement is true. In the context of algorithms and computational theory, a reduction is a technique used to demonstrate the relationship between two problems. It involves taking a known problem, Problem B, for which we already have a solution (an algorithm), and using that solution to solve a different problem, Problem A.

This approach is particularly useful in complexity theory, where one often shows that if one problem can be reduced to another, then the difficulty of solving the first problem is at most as great as the difficulty of solving the second. The essence of a reduction is that it allows us to transfer solutions and insights from one problem to another, thus establishing their computational equivalence or helping to categorize their complexity.

By relying on an algorithm for Problem B, a reduction effectively demonstrates that if we can efficiently solve Problem B, we can also apply this solution to efficiently solve Problem A. This concept underpins many important results in computer science, including NP-completeness, where one shows that if any NP problem can be reduced to another, the complexity class remains unchanged.