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A skew-symmetric graph is a graph that is isomorphic to its own transpose graph, via a special kind of isomorphism that pairs up all of the vertices. The converse relation of a binary relation is the relation that reverses the ordering of each pair of related objects. If the relation is interpreted as a directed graph, this is the same thing as ...
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):
Topological orderings of directed acyclic graphs, using a state space whose local moves reverse the ordering of two elements. [2] Spanning trees of graphs, non-crossing spanning trees of planar point sets, and more generally bases of matroids, using a state space that swaps one edge for another. [2] Euler tours in graphs. [10]
A dependency graph is a graph that has a vertex for each object to be updated, and an edge connecting two objects whenever one of them needs to be updated earlier than the other. Dependency graphs without circular dependencies form directed acyclic graphs , representations of partial orderings (in this case, across a spreadsheet) that can be ...
Depending on the problem at hand, pre-order, post-order, and especially one of the number of subtrees − 1 in-order operations may be optional. Also, in practice more than one of pre-order, post-order, and in-order operations may be required. For example, when inserting into a ternary tree, a pre-order operation is performed by comparing items.
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An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.