10 Essential Algorithms That Shaped Modern Computing

We frequently use several algorithms in everyday programming.

What Is an Algorithm?

In short, any well-defined computational steps that take one or more inputs and produce one or more outputs can be called an algorithm (source: Thomas H. Cormen, Charles E. Leiserson, "Introduction to Algorithms", 3rd edition).

Algorithms solve specific problems through a series of steps and possess three essential properties:

Finite: the algorithm must terminate after a finite number of steps.

Exact: each step must be precisely defined.

Feasible: it must solve the problem within a reasonable amount of time.

Although algorithms are widely used in computing, they originate from mathematics; the earliest known mathematical algorithms date back to the Babylonians around 1600 BC.

1. Merge Sort, Quick Sort, and Heap Sort

These three sorting algorithms each have strengths: Merge Sort (invented by John von Neumann in 1945) is a classic divide‑and‑conquer method; Quick Sort combines partitioning and divide‑and‑conquer, offering high performance on random arrays; Heap Sort uses a priority‑queue mechanism to reduce search time. Compared with early sorts like Bubble Sort, they dramatically improved data processing, enabling modern data mining, AI, link analysis, and web tools.

2. Fourier Transform and Fast Fourier Transform (FFT)

These simple yet powerful algorithms convert signals between time and frequency domains, underpinning virtually every digital technology—from the Internet and Wi‑Fi to smartphones and satellite communications. Mastery of them is essential for any computer‑related degree.

3. Dijkstra’s Shortest‑Path Algorithm

This graph‑based algorithm finds the shortest distance between two nodes and is fundamental to Internet routing and many other network problems. Although newer methods exist, Dijkstra’s stability remains unmatched.

4. RSA Asymmetric Encryption

RSA, created by the three founders of RSA Security, revolutionized key exchange and secure communication on the Internet. It enables safe transmission of sensitive data such as credit‑card information by allowing secure key sharing over insecure channels.

5. Secure Hash Algorithms (SHA)

SHA is a family of cryptographic hash functions defined by the U.S. National Institute of Standards and Technology. They protect software distribution, email, browsers, and many other applications from man‑in‑the‑middle attacks and phishing.

6. Integer Factorization

This mathematical algorithm decomposes a composite number into prime factors. It underlies many encryption schemes, including RSA, by making it computationally hard to reverse without the private key.

7. Link Analysis Algorithms

Link analysis examines relationships between web pages, social nodes, and market data. By representing a graph as a matrix and solving an eigenvalue problem, it powers Google PageRank, Facebook news‑feed ranking, LinkedIn job recommendations, YouTube video suggestions, and many other systems.

8. Proportional‑Integral‑Derivative (PID) Control Algorithm

PID control is used in aircraft, automobiles, TVs, smartphones, satellites, factories, and robots. It reduces the error between a desired setpoint and actual output by feeding back the error, its integral, and its derivative, making it indispensable for modern automation.

9. Data Compression Algorithms

Various compression techniques (e.g., MP3, JPEG, MPEG‑2) optimize storage and transmission for audio, images, video, and more. They are employed not only in file archives but also in web page delivery, gaming, cloud storage, and many other systems to improve efficiency.

10. Pseudorandom Number Generators

True random numbers are unattainable for computers, but pseudorandom generators provide sufficient randomness for networking, cryptography, security hashes, online gaming, AI, and initializing conditions in problem solving.