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An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...
Sort the edge list lexicographically. (Here we assume that the nodes of the tree are ordered, and that the root is the first element in this order.) Construct adjacency lists for each node (called next) and a map from nodes to the first entries of the adjacency lists (called first): For each edge (u,v) in the list, do in parallel:
The time complexity of operations in the adjacency list representation can be improved by storing the sets of adjacent vertices in more efficient data structures, such as hash tables or balanced binary search trees (the latter representation requires that vertices are identified by elements of a linearly ordered set, such as integers or ...
In computer science, the Edmonds–Karp algorithm is an implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network in (| | | |) time. The algorithm was first published by Yefim Dinitz in 1970, [1] [2] and independently published by Jack Edmonds and Richard Karp in 1972. [3]
Neighbourhoods may be used to represent graphs in computer algorithms, via the adjacency list and adjacency matrix representations. Neighbourhoods are also used in the clustering coefficient of a graph, which is a measure of the average density of its neighbourhoods. In addition, many important classes of graphs may be defined by properties of ...
Provided the graph is described using an adjacency list, Kosaraju's algorithm performs two complete traversals of the graph and so runs in Θ(V+E) (linear) time, which is asymptotically optimal because there is a matching lower bound (any algorithm must examine all vertices and edges).
The adjacency matrix distributed between multiple processors for parallel Prim's algorithm. In each iteration of the algorithm, every processor updates its part of C by inspecting the row of the newly inserted vertex in its set of columns in the adjacency matrix. The results are then collected and the next vertex to include in the MST is ...
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