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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.
Parallel all-pairs shortest path algorithm; Parallel breadth-first search; Parallel single-source shortest path algorithm; Path-based strong component algorithm; Pre-topological order; Prim's algorithm; Proof-number search; Push–relabel maximum flow algorithm
If G is a tree, replacing the queue of the breadth-first search algorithm with a stack will yield a depth-first search algorithm. For general graphs, replacing the stack of the iterative depth-first search implementation with a queue would also produce a breadth-first search algorithm, although a somewhat nonstandard one. [7]
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.
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)).
The pancake sorting problem was first posed by Jacob E. Goodman, writing under the pseudonym "Harry Dweighter" ("harried waiter"). [9] Although seen more often as an educational device, pancake sorting also appears in applications in parallel processor networks, in which it can provide an effective routing algorithm between processors. [10] [11]
The patience sorting algorithm can be applied to process control. Within a series of measurements, the existence of a long increasing subsequence can be used as a trend marker. A 2002 article in SQL Server magazine includes a SQL implementation, in this context, of the patience sorting algorithm for the length of the longest increasing subsequence.