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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 ...
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.
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 ...
An example of bag structure with 23 elements. There are some special data structures that parallel BFS can benefit from, such as CSR (Compressed Sparse Row), bag-structure, bitmap and so on. 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 ...
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 ...
For a grid map from a video game, using the Taxicab distance or the Chebyshev distance becomes better depending on the set of movements available (4-way or 8-way). If the heuristic h satisfies the additional condition h ( x ) ≤ d ( x , y ) + h ( y ) for every edge ( x , y ) of the graph (where d denotes the length of that edge), then h is ...
In the analysis of algorithms, the input to breadth-first search is assumed to be a finite graph, represented as an adjacency list, adjacency matrix, or similar representation. However, in the application of graph traversal methods in artificial intelligence the input may be an implicit representation of an infinite graph. In this context, a ...
Execute the following three operations in a certain order: [5] N: Visit the current node. L: Recursively traverse the current node's left subtree. R: Recursively traverse the current node's right subtree. The trace of a traversal is called a sequentialisation of the tree. The traversal trace is a list of each visited node.