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SMA* or Simplified Memory Bounded A* is a shortest path algorithm based on the A* algorithm. The main advantage of SMA* is that it uses a bounded memory, while the A* algorithm might need exponential memory.
The space complexity of A* is roughly the same as that of all other graph search algorithms, as it keeps all generated nodes in memory. [1] In practice, this turns out to be the biggest drawback of the A* search, leading to the development of memory-bounded heuristic searches, such as Iterative deepening A* , memory-bounded A*, and SMA* .
The most general version of the DPOP algorithm: "MB-DPOP: A New Memory-Bounded Algorithm for Distributed Optimization " (with Adrian Petcu), Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI), pp. 1452–1457, 2007
The edges traversed in this search form a Trémaux tree, a structure with important applications in graph theory. Performing the same search without remembering previously visited nodes results in visiting nodes in the order A, B, D, F, E, A, B, D, F, E, etc. forever, caught in the A, B, D, F, E cycle and never reaching C or G.
Iterative deepening A* (IDA*) is a graph traversal and path search algorithm that can find the shortest path between a designated start node and any member of a set of goal nodes in a weighted graph.
Specific applications of search algorithms include: Problems in combinatorial optimization, such as: . The vehicle routing problem, a form of shortest path problem; The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as ...
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Memory bound refers to a situation in which the time to complete a given computational problem is decided primarily by the amount of free memory required to hold the working data. This is in contrast to algorithms that are compute-bound , where the number of elementary computation steps is the deciding factor.