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Best-first search is a class of search algorithms which explores a graph by expanding the most promising node chosen according to a specified rule.. Judea Pearl described best-first search as estimating the promise of node n by a "heuristic evaluation function () which, in general, may depend on the description of n, the description of the goal, the information gathered by the search up to ...
A* is an informed search algorithm, or a best-first search, meaning that it is formulated in terms of weighted graphs: starting from a specific starting node of a graph, it aims to find a path to the given goal node having the smallest cost (least distance travelled, shortest time, etc.).
Examples of such greedy algorithms are Kruskal's algorithm and Prim's algorithm for finding minimum spanning trees and the algorithm for finding optimum Huffman trees. Greedy algorithms appear in the network routing as well. Using greedy routing, a message is forwarded to the neighbouring node which is "closest" to the destination.
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Beam search is a modification of best-first search that reduces its memory requirements. Best-first search is a graph search which orders all partial solutions (states) according to some heuristic. But in beam search, only a predetermined number of best partial solutions are kept as candidates. [1] It is thus a greedy algorithm.
The best lower bound known for any deterministic online algorithm is 10/3. [2] Unit weight undirected graphs can be explored with a competitive ration of 2 − ε, [3] which is already a tight bound on Tadpole graphs. [4] In the directed case, the greedy tour is at most (n − 1)-times longer than an optimal tour.
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In fact, if the search graph is given cost ′ (,) = (,) + () for a consistent , then A* is equivalent to best-first search on that graph using Dijkstra's algorithm. [3] In the unusual event that an admissible heuristic is not consistent, a node will need repeated expansion every time a new best (so-far) cost is achieved for it.