Polynomial time is a term used in computer science to describe the efficiency of an algorithm. Specifically, an algorithm is said to run in polynomial time if the number of steps required to complete the algorithm for a given input is bounded by a polynomial function of the size of the input. In layman’s terms, it means that the time it takes for the algorithm to run grows at a “reasonable” rate as the size of the input increases.

In computational complexity theory, algorithms that run in polynomial time are denoted by the complexity class $P$. Polynomial-time algorithms are considered to be “efficient” because their running time increases at a manageable rate as the size of the problem (i.e., the input) increases.

This concept is particularly important when comparing classical algorithms to quantum algorithms. For example, Shor’s Algorithm, which can factor integers in polynomial time, has significant implications for cryptography because it can efficiently break encryption schemes like RSA, which rely on the difficulty of factoring large composite numbers.

Key Takeaways:

• Polynomial time is a metric for evaluating algorithmic efficiency.
• Algorithms that operate in polynomial time are scalable and well-suited for handling large, complex problems.
• CXOs should be aware of whether the algorithms they rely on for critical business functions operate in polynomial time to ensure efficiency and scalability.