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An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):
Kahn's algorithm for topological sorting builds the vertex ordering directly. It maintains a list of vertices that have no incoming edges from other vertices that have not already been included in the partially constructed topological ordering; initially this list consists of the vertices with no incoming edges at all.
The traditional ld (Unix linker) requires that its library inputs be sorted in topological order, since it processes files in a single pass. This applies both to static libraries ( *.a ) and dynamic libraries ( *.so ), and in the case of static libraries preferably for the individual object files contained within.
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
A Kahn process network (KPN, or process network) is a distributed model of computation in which a group of deterministic sequential processes communicate through unbounded first in, first out channels. The model requires that reading from a channel is blocking while writing is non-blocking.
The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points, syntactic analysis (e.g., top-down parsers), and computing the discrete Fourier transform .
Tournament sort is a sorting algorithm.It improves upon the naive selection sort by using a priority queue to find the next element in the sort. In the naive selection sort, it takes O(n) operations to select the next element of n elements; in a tournament sort, it takes O(log n) operations (after building the initial tournament in O(n)).
Robert Elliot Kahn (born December 23, 1938) is an American electrical engineer who, along with Vint Cerf, first proposed the Transmission Control Protocol (TCP) and the Internet Protocol (IP), the fundamental communication protocols at the heart of the Internet.