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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.
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 ...
In the example on the left, there are two arrays, C and R. Array C stores the adjacency lists of all nodes. Array R stored the index in C, the entry R[i] points to the beginning index of adjacency lists of vertex i in array C. The CSR is extremely fast because it costs only constant time to access vertex adjacency.
In the context of efficient representations of graphs, J. H. Muller defined a local structure or adjacency labeling scheme for a graph G in a given family F of graphs to be an assignment of an O(log n)-bit identifier to each vertex of G, together with an algorithm (that may depend on F but is independent of the individual graph G) that takes as input two vertex identifiers and determines ...
1 S ← empty sequence 2 u ← target 3 if prev[u] is defined or u = source: // Proceed if the vertex is reachable 4 while u is defined: // Construct the shortest path with a stack S 5 insert u at the beginning of S // Push the vertex onto the stack 6 u ← prev[u] // Traverse from target to source
The adjacency lists for the remaining nodes that could not be found in H need to be fetched. A scan over L ( t − 1 ) {\displaystyle L(t-1)} yields the partition identifiers. After sorting and deletion of duplicates, the respective files F i {\displaystyle F_{i}} can be concatenated into a temporary file F' .
A* is often used for the common pathfinding problem in applications such as video games, but was originally designed as a general graph traversal algorithm. [4] It finds applications in diverse problems, including the problem of parsing using stochastic grammars in NLP. [26] Other cases include an Informational search with online learning. [27]
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).