For some problems, A* produces too large an open list. IDA* may suffer from keeping too little information: in a search graph with many paths to a given node, IDA* must re-search from that node.
One solution is to limit the size of open; this is called a beam search. Tha algorithms MA* and SMA* remove the worst and oldest node from open when a new space is needed, while choosing the best and newest node to expand at each step.
Beam search provides the directedness of depth-first search while maintaining several open lines of search (the width of the beam). For some applications (particularly those dealing with continuous time functions, such as signal understanding), it is necessary to prune less-promising search paths in order to keep storage and time requirements manageable. At the same time, it may be necessary to carry more than one line of search in case the current ``best'' line is not the overall best path.
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