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  2. Adjacency list - Wikipedia

    en.wikipedia.org/wiki/Adjacency_list

    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.

  3. Depth-first search - Wikipedia

    en.wikipedia.org/wiki/Depth-first_search

    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.

  4. Breadth-first search - Wikipedia

    en.wikipedia.org/wiki/Breadth-first_search

    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 ...

  5. Nested set model - Wikipedia

    en.wikipedia.org/wiki/Nested_set_model

    The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases.. It is based on Nested Intervals, that "are immune to hierarchy reorganization problem, and allow answering ancestor path hierarchical queries algorithmically — without accessing the stored hierarchy relation".

  6. Dijkstra's algorithm - Wikipedia

    en.wikipedia.org/wiki/Dijkstra's_algorithm

    1 function Dijkstra(Graph, source): 2 3 for each vertex v in Graph.Vertices: 4 dist[v] ← INFINITY 5 prev[v] ← UNDEFINED 6 add v to Q 7 dist[source] ← 0 8 9 while Q is not empty: 10 u ← vertex in Q with minimum dist[u] 11 remove u from Q 12 13 for each neighbor v of u still in Q: 14 alt ← dist[u] + Graph.Edges(u, v) 15 if alt < dist[v ...

  7. Tarjan's strongly connected components algorithm - Wikipedia

    en.wikipedia.org/wiki/Tarjan's_strongly_connected...

    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 any nodes that have not yet been found). As usual with depth-first search, the search visits every node of the graph exactly once, refusing to revisit any node that has already been visited.

  8. Iterative deepening depth-first search - Wikipedia

    en.wikipedia.org/wiki/Iterative_deepening_depth...

    In computer science, iterative deepening search or more specifically iterative deepening depth-first search [1] (IDS or IDDFS) is a state space/graph search strategy in which a depth-limited version of depth-first search is run repeatedly with increasing depth limits until the goal is found.

  9. Parallel breadth-first search - Wikipedia

    en.wikipedia.org/wiki/Parallel_breadth-first_search

    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.