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The same idea of using a DAG to represent a family of paths occurs in the binary decision diagram, [55] [56] a DAG-based data structure for representing binary functions. In a binary decision diagram, each non-sink vertex is labeled by the name of a binary variable, and each sink and each edge is labeled by a 0 or 1.
In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...
The main operation performed by the adjacency list data structure is to report a list of the neighbors of a given vertex. Using any of the implementations detailed above, this can be performed in constant time per neighbor. In other words, the total time to report all of the neighbors of a vertex v is proportional to the degree of v.
The data structure is typically stored as a Boolean matrix, so if matrix[1][4] = true, then it is the case that node 1 can reach node 4 through one or more hops. The transitive closure of the adjacency relation of a directed acyclic graph (DAG) is the reachability relation of the DAG and a strict partial order.
The canonical application of topological sorting is in scheduling a sequence of jobs or tasks based on their dependencies.The jobs are represented by vertices, and there is an edge from x to y if job x must be completed before job y can be started (for example, when washing clothes, the washing machine must finish before we put the clothes in the dryer).
Rooted trees, often with an additional structure such as an ordering of the neighbors at each vertex, are a key data structure in computer science; see tree data structure. In a context where trees typically have a root, a tree without any designated root is called a free tree. A labeled tree is a tree in which each vertex is given a unique label.
The main alternative data structure, also in use for this application, is the adjacency list. [ 11 ] [ 12 ] The space needed to represent an adjacency matrix and the time needed to perform operations on them is dependent on the matrix representation chosen for the underlying matrix.
A GADDAG is a data structure presented by Steven Gordon in 1994, for use in generating moves for Scrabble and other word-generation games where such moves require words that "hook into" existing words.