A space–time or time–memory trade-off in computer science is a case where an algorithm or programtrades increased space usage with decreased time. Here, space refers to the data storage consumed in performing a given task, and time refers to the time consumed in performing a given task. The utility of a given space–time tradeoff is affected by related fixed and variable costs, and is subject to diminishing returns.
History
Biological usage of time–memory tradeoffs can be seen in the earlier stages of animal behavior. Using stored knowledge or encoding stimuli reactions as "instincts" in the DNA avoids the need for "calculation" in time-critical situations. More specific to computers, look-up tables have been implemented since the very earliest operating systems. In 1980 Martin Hellman first proposed using a time–memory tradeoff for cryptanalysis.
Types of tradeoff
Lookup tables vs. recalculation
A common situation is an algorithm involving a lookup table: an implementation can include the entire table, which reduces computing time, but increases the amount of memory needed, or it can compute table entries as needed, increasing computing time, but reducing memory requirements.
A space–time tradeoff can be applied to the problem of data storage. If data is stored uncompressed, it takes more space but access takes less time than if the data were stored compressed. Depending on the particular instance of the problem, either way is practical. There are also rare instances where it is possible to directly work with compressed data, such as in the case of compressed bitmap indices, where it is faster to work with compression than without compression.
Storing only the SVG source of a vector image and rendering it as a bitmap image every time the page is requested would be trading time for space; more time used, but less space. Rendering the image when the page is changed and storing the rendered images would be trading space for time; more space used, but less time. This technique is more generally known as caching.
Larger code size can be traded for higher program speed when applying loop unrolling. This technique makes the code longer for each iteration of a loop, but saves the computation time required for jumping back to the beginning of the loop at the end of each iteration.
Other examples
Algorithms that also make use of space–time tradeoffs include:
