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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.
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 ...
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.
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' .
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 ...
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[8] [9] Another problem related to reachability queries is in quickly recalculating changes to reachability relationships when some portion of the graph is changed. For example, this is a relevant concern to garbage collection which needs to balance the reclamation of memory (so that it may be reallocated) with the performance concerns of the ...