One-pass algorithm

In computing, a one-pass algorithm or single-pass algorithm is a streaming algorithm which reads its input exactly once.^[1] It does so by processing items in order, without unbounded buffering; it reads a block into an input buffer, processes it, and moves the result into an output buffer for each step in the process.^[2] A one-pass algorithm generally requires O(n) (see 'big O' notation) time and less than O(n) storage (typically O(1)), where n is the size of the input.^[3] An example of a one-pass algorithm is the Sondik partially observable Markov decision process.^[4]

Example problems solvable by one-pass algorithms

Given any list as an input:

• Count the number of elements.

Given a list of numbers:

• Find the k largest or smallest elements, k given in advance.
• Find the sum, mean, variance and standard deviation of the elements of the list. See also Algorithms for calculating variance.

Given a list of symbols from an alphabet of k symbols, given in advance.

• Count the number of times each symbol appears in the input.
• Find the most or least frequent elements.
• Sort the list according to some order on the symbols (possible since the and after number of symbols is limited).
• Find the maximum gap between two appearances of a given symbol.

Example problems not solvable by one-pass algorithms

Given any list as an input:

• Find the nth element from the end (or report that the list has fewer than n elements).
• Find the middle element of the list. However, this is solvable with two passes: Pass 1 counts the elements and pass 2 picks out the middle one.

Given a list of numbers:

• Find the median.
• Find the modes (This is not the same as finding the most frequent symbol from a limited alphabet).
• Sort the list.
• Count the number of items greater than or less than the mean. However, this can be done in constant memory with two passes: Pass 1 finds the average and pass 2 does the counting.

The two-pass algorithms above are still streaming algorithms but not one-pass algorithms.

References

1. Schweikardt, Nicole. "One-Pass Algorithm" (PDF). Retrieved 2021-07-01.
2. Pollett, Chris (2005-03-14). "One and Two Pass Algorithms" (PDF). Retrieved 2021-07-01.
3. Schweikardt, Nicole (2009), "One-Pass Algorithm", in LIU, LING; ÖZSU, M. TAMER (eds.), Encyclopedia of Database Systems, Boston, MA: Springer US, pp. 1948–1949, doi:10.1007/978-0-387-39940-9_253, ISBN 978-0-387-39940-9, retrieved 2021-04-13
4. "Sondik's One-Pass Algorithm". www.pomdp.org.