An adaptive algorithm is an algorithm that changes its behavior based on information available at the time it is run. This might be information about computational resources available, or the history of data recently received.
For example, stable partition, using no additional memory is O(n lg n) but given O(n) memory, it can be O(n) in time. As implemented by the C++ Standard Library,
stable_partition is adaptive and so it acquires as much memory as it can get (up to what it would need at most) and applies the algorithm using that available memory. Another example is adaptive sort, whose behaviour changes upon the presortedness of its input.
In machine learning and optimization, many algorithms are adaptive or have adaptive variants, which usually means that the algorithm parameters are automatically adjusted according to statistics about the optimisation thus far (e.g. the rate of convergence). Examples include adaptive simulated annealing, adaptive coordinate descent, AdaBoost, and adaptive quadrature.
In data compression, adaptive coding algorithms such as Adaptive Huffman coding or Prediction by partial matching can take a stream of data as input, and adapt their compression technique based on the symbols that they have already encountered.
In signal processing, the Adaptive Transform Acoustic Coding (ATRAC) codec used in MiniDisc recorders is called "adaptive" because the window length (the size of an audio "chunk") can change according to the nature of the sound being compressed, to try and achieve the best-sounding compression strategy.
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