Search results
Results from the WOW.Com Content Network
Then, 8| E | > | V | 2 /8 when | E |/| V | 2 > 1/64, that is the adjacency list representation occupies more space than the adjacency matrix representation when d > 1/64. Thus a graph must be sparse enough to justify an adjacency list representation. Besides the space trade-off, the different data structures also facilitate different operations.
Any vertex that is not on a directed cycle forms a strongly connected component all by itself: for example, a vertex whose in-degree or out-degree is 0, or any vertex of an acyclic graph. The basic idea of the algorithm is this: a depth-first search (DFS) begins from an arbitrary start node (and subsequent depth-first searches are conducted on ...
For external memory algorithms the external memory model by Aggarwal and Vitter [1] is used for analysis. A machine is specified by three parameters: M, B and D.M is the size of the internal memory, B is the block size of a disk and D is the number of parallel disks.
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
In computer science, the Hopcroft–Karp algorithm (sometimes more accurately called the Hopcroft–Karp–Karzanov algorithm) [1] is an algorithm that takes a bipartite graph as input and produces a maximum-cardinality matching as output — a set of as many edges as possible with the property that no two edges share an endpoint.
For each vertex we store the list of adjacencies (out-edges) in order of the planarity of the graph (for example, clockwise with respect to the graph's embedding). We then initialize a counter = + and begin a Depth-First Traversal from . During this traversal, the adjacency list of each vertex is visited from left-to-right as needed.
Input: A graph G and a starting vertex root of G. Output: Goal state.The parent links trace the shortest path back to root [9]. 1 procedure BFS(G, root) is 2 let Q be a queue 3 label root as explored 4 Q.enqueue(root) 5 while Q is not empty do 6 v := Q.dequeue() 7 if v is the goal then 8 return v 9 for all edges from v to w in G.adjacentEdges(v) do 10 if w is not labeled as explored then 11 ...
In the CSR, all adjacencies of a vertex is sorted and compactly stored in a contiguous chunk of memory, with adjacency of vertex i+1 next to the adjacency of i. In the example on the left, there are two arrays, C and R. Array C stores the adjacency lists of all nodes.