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For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 ≡ 4 (mod 6). Equivalently, n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 1–2–4 loop (the inverse of the 4–2–1 loop of the unaltered function f defined in the Statement of the problem section of ...
The program evaluation and review technique (PERT) is a statistical tool used in project management, which was designed to analyze and represent the tasks involved in completing a given project. PERT was originally developed by Charles E. Clark for the United States Navy in 1958; it is commonly used in conjunction with the Critical Path Method ...
1) An ant chooses a path among all possible paths and lays a pheromone trail on it. 2) All the ants are travelling on different paths, laying a trail of pheromones proportional to the quality of the solution. 3) Each edge of the best path is more reinforced than others. 4) Evaporation ensures that the bad solutions disappear.
A* search algorithm. A* (pronounced "A-star") is a graph traversal and pathfinding algorithm, which is used in many fields of computer science due to its completeness, optimality, and optimal efficiency. [1] Given a weighted graph, a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from ...
In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. [1][2][3] Contour integration is closely related to the calculus of residues, [4] a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are ...
Dijkstra's algorithm (/ ˈdaɪkstrəz / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. [4][5][6] Dijkstra's algorithm finds the shortest path from a ...
The Viterbi algorithm is named after Andrew Viterbi, who proposed it in 1967 as a decoding algorithm for convolutional codes over noisy digital communication links. [2] It has, however, a history of multiple invention, with at least seven independent discoveries, including those by Viterbi, Needleman and Wunsch, and Wagner and Fischer. [3]
2-satisfiability. In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables. It is a special case of the general Boolean satisfiability problem, which can involve constraints on ...