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In computer programming, an algorithm is a set of instructions that precisely specifies how to solve a problem. Algorithms can be solved by hand or through computers and they are used for a wide range of problems including placing the tiles of a mosaics, calculating optimal routes for delivery trucks, and even solving chess problems. While some algorithms have been around for hundreds or even thousands of years these days it is not uncommon to find new ones being developed in academic journals on a daily basis. These algorithms currently number in the tens if not hundreds of thousands and offer solutions to almost any imaginable problem from predicting lunar eclipses from different locations to estimating how much time will pass before the next asteroid strikes Earth. The following is a list of the top ten algorithms sorted by the number of academic papers written about them. Graph theory is a field of mathematics that deals with graphs whose elements are vertices (also called nodes) and edges (also called arcs or lines). This highly interdisciplinary field provides a theoretical foundation for such diverse areas as social network analysis, molecular biology, and computer science. While graph theory itself has been around since the 18th century, many of its most useful applications were not discovered until the late 20th century. Today there are hundreds if not thousands of algorithms related to graph theory and this list includes some of the more influential ones sorted by number of academic publications written about them. Set theory is a branch of mathematics that studies sets, which informally are collections of objects. A set is defined informally as "a collection of distinct objects" and the study of sets and their properties is called set theory. The field evolved from questions about the natural numbers: what properties can be ascribed to a set (or collection) of them; e.g., what makes a countable collection (or "set") into a mathematical object rather than just a haphazard list? Are such collections themselves useful in some way? The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. Today the subject is a major area of research in mathematics, with deep connections to abstract algebra, topology, function theory, and analysis. The following are some notable algorithms related to set theory sorted by number of academic papers written about them. Quantum computing is the use of quantum-mechanical phenomena such as superposition and entanglement to perform computation. Quantum computers are different from binary digital electronic computers based on transistors because they use quantum-mechanical phenomena to represent data. Since the principles of quantum mechanics are counterintuitive, the development of these devices is necessarily vague. Recent attempts to use quantum computation have struggled with problems such as how to program the system so that it can be executed algorithmically. While theoretical work at first seemed disconnected from any practical need, there has been an emerging field called quantum machine learning. Quantum machine learning is concerned with algorithms that utilize probabilistic models based on quantum states to learn high-dimensional problems. The following is a list of the most influential algorithms related to quantum computing sorted by number of academic papers written about them. cfa1e77820
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