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The canonical application of topological sorting is in scheduling a sequence of jobs or tasks based on their dependencies.The jobs are represented by vertices, and there is an edge from x to y if job x must be completed before job y can be started (for example, when washing clothes, the washing machine must finish before we put the clothes in the dryer).
Therefore, the order in which the strongly connected components are identified constitutes a reverse topological sort of the DAG formed by the strongly connected components. [7] Donald Knuth described Tarjan's SCC algorithm as one of his favorite implementations in the book The Stanford GraphBase. [8] He also wrote: [9]
Topological sorting is the algorithmic problem of finding a topological ordering of a given DAG. It can be solved in linear time. [16] Kahn's algorithm for topological sorting builds the vertex ordering directly.
The tsort program is a command line utility on Unix and Unix-like platforms, that performs a topological sort on its input. As of 2017 [update] , it is part of the POSIX .1 standard. [ 1 ]
Bitonic mergesort is a parallel algorithm for sorting. It is also used as a construction method for building a sorting network.The algorithm was devised by Ken Batcher.The resulting sorting networks consist of ( ()) comparators and have a delay of ( ()), where is the number of items to be sorted. [1]
Microsoft has unveiled a new chip called Majorana 1 that it says will enable the creation of quantum computers able to solve "meaningful, industrial-scale problems in years, not decades".
Thus, any algorithm that derives a correct topological order derives a correct evaluation order. Assume the simple calculator from above once more. Given the equation system "A = B+C; B = 5+D; C=4; D=2;", a correct evaluation order would be (D, C, B, A). However, (C, D, B, A) is a correct evaluation order as well.
Cubesort is a parallel sorting algorithm that builds a self-balancing multi-dimensional array from the keys to be sorted. As the axes are of similar length the structure resembles a cube. After each key is inserted the cube can be rapidly converted to an array. [1] A cubesort implementation written in C was published in 2014. [2]