Description
A* uses a best-first search and finds a least-cost path from a given initial node to one goal node (out of one or more possible goals). As A* traverses the graph, it follows a path of the lowest known heuristic cost, keeping a sorted priority queue of alternate path segments along the way.
It uses a distance-plus-cost heuristic function of node (usually denoted ) to determine the order in which the search visits nodes in the tree. The distance-plus-cost heuristic is a sum of two functions:
- the path-cost function, which is the cost from the starting node to the current node (usually denoted )
- an admissible "heuristic estimate" of the distance from to the goal (usually denoted ).
The part of the function must be an admissible heuristic; that is, it must not overestimate the distance to the goal. Thus, for an application like routing, might represent the straight-line distance to the goal, since that is physically the smallest possible distance between any two points or nodes.
If the heuristic h satisfies the additional condition for every edge x, y of the graph (where d denotes the length of that edge), then h is called monotone, or consistent. In such a case, A* can be implemented more efficiently—roughly speaking, no node needs to be processed more than once (see closed set below)—and A* is equivalent to running Dijkstra's algorithm with the reduced cost .
Read more about this topic: A* Search Algorithm
Famous quotes containing the word description:
“The next Augustan age will dawn on the other side of the Atlantic. There will, perhaps, be a Thucydides at Boston, a Xenophon at New York, and, in time, a Virgil at Mexico, and a Newton at Peru. At last, some curious traveller from Lima will visit England and give a description of the ruins of St. Paul’s, like the editions of Balbec and Palmyra.”
—Horace Walpole (1717–1797)
“An intentional object is given by a word or a phrase which gives a description under which.”
—Gertrude Elizabeth Margaret Anscombe (b. 1919)
“Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.”
—Willard Van Orman Quine (b. 1908)