## Graph algorithms

In computer science, A* (pronounced "Ay star") is a graph search algorithm that finds a path from a given initial node to a given goal node (or one passing a given goal test). It employs a "heuristic estimate" that ranks each node by an estimate of the best route that goes through that node. It visits the nodes in order of this heuristic estimate. The A* algorithm is therefore an example of best-first search.. ...more on Wikipedia about "A* search algorithm"

The Bellman-Ford algorithm computes single-source shortest paths in a weighted digraph (where some of the edge weights may be negative). Dijkstra's algorithm accomplishes the same problem with a lower running time, but requires edge weights to be non-negative. Thus, Bellman-Ford is usually used only when there are negative edge weights. ...more on Wikipedia about "Bellman-Ford algorithm"

Borůvka's algorithm is an algorithm for finding minimum spanning trees. ...more on Wikipedia about "Borůvka's algorithm"

Dijkstra's algorithm, named after its discoverer, Dutch computer scientist Edsger Dijkstra, is an algorithm that solves the single-source shortest path problem for a directed graph with nonnegative edge weights. ...more on Wikipedia about "Dijkstra's algorithm"

In computer science and graph theory, the Edmonds-Karp algorithm is an implementation of the Ford-Fulkerson method for computing the maximum flow in a flow network. The distinguishing feature is that the shortest augmenting path is used at each step, which guarantees that the computation will terminate. In most implementations, the shortest augmenting path is found using a breadth-first search, which gives a running time of $O\left(VE^2\right)$. It is asymptotically slower than the relabel-to-front algorithm, which runs in $O\left(V^3\right)$, but it is often faster in practise for sparse graphs. The algorithm was first published by a Russian scientist, Dinic, in 1970, and later, independently, by Edmonds and Karp who published it in 1972. Dinic' algorithm includes additional techniques that reduce the running time to $O\left(V^2E\right)$. ...more on Wikipedia about "Edmonds-Karp algorithm"

A flooding algorithm is an algorithm for distributing material to every part of a connected network. The name derives from the concept of inundation by a flood. ...more on Wikipedia about "Flooding algorithm"

In computer science, the Floyd-Warshall algorithm (sometimes known as the Roy-Floyd algorithm) is an algorithm for solving the all-pairs shortest path problem on weighted, directed graphs in cubic time. ...more on Wikipedia about "Floyd-Warshall algorithm"

The Ford-Fulkerson algorithm (named for L. R. Ford and D. R. Fulkerson) computes the maximum flow in a flow network. The name Ford-Fulkerson is often also used for the Edmonds-Karp algorithm, which is a specialisation of Ford-Fulkerson. ...more on Wikipedia about "Ford-Fulkerson algorithm"

In computer science a graph exploration algorithm specifies a possible way a graph can be traversed. The two most common algorithms are breadth-first search and depth-first search. ...more on Wikipedia about "Graph exploration algorithm"

Johnson's algorithm is a way to solve the all-pairs shortest path problem in a sparse, weighted, directed graph. ...more on Wikipedia about "Johnson's algorithm"

Kruskal's algorithm is an algorithm in graph theory that finds a minimum spanning tree for a connected weighted graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. If the graph is not connected, then it finds a minimum spanning forest (a minimum spanning tree for each connected component). Kruskal's algorithm is an example of a greedy algorithm. ...more on Wikipedia about "Kruskal's algorithm"

The maximum flow problem is finding a legal flow through a flow network that is maximal. Sometimes it is defined as finding the value of such a flow. The maximum flow problem can be seen as special case of more complex network flow problems. It is the multi-commodity flow problem with only one commodity, and it is the minimum-cost flow problem with all costs set to zero. The maximal flow is related to the cuts in a network by the Max-flow min-cut theorem. ...more on Wikipedia about "Maximum flow problem"

The nearest neighbour algorithm was one of the first algorithms used to determine a solution to the traveling salesman problem, and usually comes to within twenty percent of the optimal route. It is also a lot faster than testing every route and some other algorithms. ...more on Wikipedia about "Nearest neighbour algorithm"

In graph theory, a network flow is an assignment of flow to the edges of a directed graph (called a flow network in this case) where each edge has a capacity, such that the amount of flow along an edge does not exceed its capacity. In addition you have the restriction that the amount of flow into a node equals the amount of flow out of it, except if it is a source, which only has outgoing flow, or sink, which has only incomming flow. A flow network can be used to simulate traffic in a road system, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes. ...more on Wikipedia about "Network flow"

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A nonblocking minimal spanning switch is a piece of machinery, a "switch" that uses a particular algorithm to make connections. The most familiar use of switches of this type is in a telephone exchange. A switching system arranges connections between a set of information sources, and another set of information sinks. ...more on Wikipedia about "Nonblocking minimal spanning switch"

Prim's algorithm is an algorithm in graph theory that finds a minimum spanning tree for a connected weighted graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. If the graph is not connected, then it will only find a minimum spanning tree for one of the connected components. The algorithm was discovered in 1930 by mathematician Vojtech Jarnik and later independently by computer scientist Robert C. Prim in 1957 and rediscovered by Dijkstra in 1959. Therefore it is sometimes called DJP algorithm or Jarnik algorithm. ...more on Wikipedia about "Prim's algorithm"

The relabel-to-front algorithm finds the maximum flow in a flow network in $O\left(V^3\right)$ time. It is in the class of push-relabel algorithms for maximum flow which run in $O\left(V^2 E\right)$. For dense graphs it is more efficient than the Edmonds-Karp algorithm, which runs in $O\left(VE^2\right) \sube O\left(V^5\right)$ time. ...more on Wikipedia about "Relabel-to-front algorithm"

In computer science, Tarjan's off-line least common ancestors algorithm is an algorithm based on the least common ancestor property. ...more on Wikipedia about "Tarjan's off-line least common ancestors algorithm"

In graph theory, a topological sort of a directed acyclic graph (DAG) is a linear ordering of its nodes which is compatible with the partial order R induced on the nodes where x comes before y (xRy) if there's a directed path from x to y in the DAG. An equivalent definition is that each node comes before all nodes to which it has edges. Every DAG has at least one topological sort, and may have many. ...more on Wikipedia about "Topological sorting"

In mathematics, the transitive reduction of a binary relation R on a set X is the smallest relation $R\text{'}$ on X such that that the transitive closure of $R\text{'}$ is the same as the transitive closure of R. If the transitive closure of R is antisymmetric and finite, then $R\text{'}$ is unique. ...more on Wikipedia about "Transitive reduction"

In computer science, uniform-cost search (UCS) is a tree search algorithm used for traversing or searching a weighted tree, tree structure, or graph. Intuitively, the search begins at the root node. The search continues by visiting the next node which has the least total cost from the root. Nodes are visited in this manner until the goal state is reached. In this manner, uniform-cost search resembles a breadth-first fashion of traversal. ...more on Wikipedia about "Uniform-cost search" Can you feel it? http://www.shortopedia.com.

In computer science, the vertex cover problem or node cover problem is an NP-complete problem in complexity theory, and was one of Karp's 21 NP-complete problems. ...more on Wikipedia about "Vertex cover problem"