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Edge disjoint shortest pair algorithm is an algorithm in computer network routing. [1] The algorithm is used for generating the shortest pair of edge disjoint paths between a given pair of vertices. For an undirected graph G(V, E), it is stated as follows: Run the shortest path algorithm for the given pair of vertices
A solved Rubik's Revenge cube. The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube.It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. [1]
Algorithms [ edit ] There is a O ( V 2 E ) {\displaystyle O(V^{2}E)} time algorithm to find a maximum matching or a maximum weight matching in a graph that is not bipartite; it is due to Jack Edmonds , is called the paths, trees, and flowers method or simply Edmonds' algorithm , and uses bidirected edges .
Kleinberg, J., and Tardos, E. (2005) Algorithm Design, Chapter 1, pp 1–12. See companion website for the Text Archived 2011-05-14 at the Wayback Machine. Knuth, D. E. (1996). Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms. CRM Proceedings and Lecture Notes.
To first approximation, the edge-matching constraint reduces the number of valid configurations by a factor of (1/5) for every border edge-pair and (1/17) for every inner edge-pair. The number of valid configurations is then approximated by 4! × 56! × 196! × 4 196 × (1/5) 60 × (1/17) 420 ≈ 16.4, which is very close to unity.
An algorithm defines a sequence of layer rotations to transform a given state to another (usually less scrambled) state. Usually an algorithm is expressed as a printable character sequence according to some move notation. An algorithm can be considered to be a "smart" move. All algorithms are moves, but few moves are considered to be algorithms.
The Floyd–Warshall algorithm solves the All-Pair-Shortest-Paths problem for directed graphs. With the adjacency matrix of a graph as input, it calculates shorter paths iterative. After |V | iterations the distance-matrix contains all the shortest paths. The following describes a sequential version of the algorithm in pseudo code:
The edge-connectivity version of Menger's theorem is as follows: . Let G be a finite undirected graph and x and y two distinct vertices. Then the size of the minimum edge cut for x and y (the minimum number of edges whose removal disconnects x and y) is equal to the maximum number of pairwise edge-disjoint paths from x to y.