computer science

List of algorithms

List of algorithms is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand List of algorithms rather than just read about it. In short: An algorithm is a fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem or a broad set of problems. Simply speaking, algorithms define different processes, sets of rules and regulations, or methodologies that are to be followed through in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem…

Key takeaways

List of algorithms belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect List of algorithms to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of List of algorithms from memory before moving on to harder problems.

Reference excerpt

An algorithm is a fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem or a broad set of problems. Simply speaking, algorithms define different processes, sets of rules and regulations, or methodologies that are to be followed through in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations. With the increasing automation of services, more and more decisions are being made by algorithms. Some general examples are risk assessments, anticipatory policing, and pattern recognition technology. The following is a list of well-known algorithms.

Automated planning

Combinatorial algorithms

General combinatorial algorithms Brent's algorithm: finds a cycle in function value iterations using only two iterators Floyd's cycle-finding algorithm: finds a cycle in function value iterations Gale–Shapley algorithm: solves the stable matching problem Pseudorandom number generators (uniformly distributed—see also List of pseudorandom number generators for other PRNGs with varying degrees of convergence and varying statistical quality): ACORN generator Blum Blum Shub Lagged Fibonacci generator Linear congruential generator Mersenne Twister

Graph algorithms

Blossom algorithm: algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject to constraints, e.g. proper coloring or list coloring) Hopcroft–Karp algorithm: convert a bipartite graph to a maximum-cardinality matching Hungarian algorithm: algorithm for finding a perfect matching Prüfer coding: conversion between a labeled tree and its Prüfer sequence Tarjan's off-line lowest common ancestors algorithm: computes lowest common ancestors for pairs of nodes in a tree Topological sort: finds linear order of nodes (e.g. jobs) based on their dependencies.

Graph drawing

Coin graph drawing algorithms for finite connected planar graphs (approximately computing the theoretical circle-packing given by the Koebe-Andreev-Thurston theorem). See also Fáry's theorem on straight-line drawings of planar graphs. Force-based algorithms (also known as force-directed algorithms or spring-based algorithms) Spectral layout

Network theory

Network analysis Link analysis Girvan–Newman algorithm: detect communities in complex systems Web link analysis Hyperlink-Induced Topic Search (HITS) (also known as Hubs and authorities) PageRank TrustRank Flow networks Dinic's algorithm: is a strongly polynomial algorithm for computing the maximum flow in a flow network. Edmonds–Karp algorithm: implementation of Ford–Fulkerson Ford–Fulkerson algorithm: computes the maximum flow in a graph Karger's algorithm: a Monte Carlo method to compute the minimum cut of a connected graph Push–relabel algorithm: computes a maximum flow in a graph

Routing for graphs Edmonds' algorithm (also known as Chu–Liu/Edmonds' algorithm): find maximum or minimum branchings Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane Longest path problem: find a simple path of maximum length in a given graph Minimum spanning tree Borůvka's algorithm Kruskal's algorithm Prim's algorithm Reverse-delete algorithm Nonblocking minimal spanning switch say, for a telephone exchange Shortest path problem Bellman–Ford algorithm: computes shortest paths in a weighted graph (where some of the edge weights may be negative) Dijkstra's algorithm: computes shortest paths in a graph with non-negative edge weights Floyd–Warshall algorithm: solves the all pairs shortest path problem in a weighted, directed graph Johnson's algorithm: all pairs shortest path algorithm in sparse weighted directed graph Transitive closure problem: find the transitive closure of a given binary relation Traveling salesman problem Christofides algorithm Nearest neighbour algorithm Vehicle routing problem Clarke and Wright Saving algorithm Warnsdorff's rule: a heuristic method for solving the Knight's tour problem

Graph search

A*: special case of best-first search that uses heuristics to improve speed B*: a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals) Backtracking: abandons partial solutions when they are found not to satisfy a complete solution Beam search: is a heuristic search algorithm that is an optimization of best-first search that reduces its memory requirement Beam stack search: integrates backtracking with beam search Best-first search: traverses a graph in the order of likely importance using a priority queue Bidirectional search: find the shortest path from an initial vertex to a goal vertex in a directed graph Breadth-first search: traverses a graph level by level Brute-force search: an exhaustive and reliable search method, but computationally inefficient in many applications D*: an incremental heuristic search algorithm Depth-first search: traverses a graph branch by branch Dijkstra's algorithm: a special case of A* for which no heuristic function is used General Problem Solver: a seminal theorem-proving algorithm intended to work as a universal problem solver machine. Iterative deepening depth-first search (IDDFS): a state space search strategy Jump point search: an optimization to A* which may reduce computation time by an order of magnitude using further heuristics Lexicographic breadth-first search (also known as Lex-BFS): a linear time algorithm for ordering the vertices of a graph SSS*: state space search traversing a game tree in a best-first fashion similar to that of the A* search algorithm Uniform-cost search: a tree search that finds the lowest-cost route where costs vary

Subgraphs Cliques Bron–Kerbosch algorithm: a technique for finding maximal cliques in an undirected graph MaxCliqueDyn maximum clique algorithm: find a maximum clique in an undirected graph Strongly connected components Kosaraju's algorithm Path-based strong component algorithm Tarjan's strongly connected components algorithm Subgraph isomorphism problem

Sequence algorithms

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with List of algorithms

Start with the simplest possible case. Write down what List of algorithms claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to List of algorithms before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about List of algorithms ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of List of algorithms

In research: List of algorithms appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses List of algorithms in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: List of algorithms is common in secondary-school and first-year university syllabi. It links to neighbouring topics Algorithms, Mathematics-related lists, Optimization algorithms and methods, so understanding it makes those chapters shorter.
In everyday life: Look for List of algorithms outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study List of algorithms in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what List of algorithms means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain List of algorithms out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is List of algorithms in simple terms?

Why does List of algorithms matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study List of algorithms?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on List of algorithms.