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Initially introduced in the late 1960s and early 1970s, dynamic programming algorithms have become increasingly popular in automatic speech recognition. There are two reasons why this has occurred. First, the dynamic programming strategy can be combined with a very efficient and practical pruning strategy so that very large search spaces can be handled. Second, the dynamic programming strategy has turned out to be extremely flexible in adapting to new requirements. Examples of such requirements are the lexical tree organization of the pronunciation lexicon and the generation of a word graph instead of the single best sentence. We attempt to review the use of dynamic programming search strategies for large-vocabulary continuous speech recognition (LVCSR). The following methods are described in detail: searching using a lexical tree, language-model look-ahead and word-graph generation.