One-pass algorithm: Difference between revisions

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{{Short description|Type of streaming algorithm}}

In computing, a '''one-pass algorithm''' is one which reads its input exactly once, in order, without [[Buffer|buffering]]. A one-pass algorithm generally requires O(n) (see [[Big O Notation|'big O' notation]]) time and less than O(n) storage (typically O(1)), where n is the size of the input.

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[[Category:Computing]]

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In computing, a '''one-pass algorithm''' or '''single-pass algorithm''' is a [[streaming algorithm]] which reads its input exactly once.<ref name="frankfurt"/> It does so by processing items in order, without unbounded [[Buffer (computer science)|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.<ref name="sjsu"/> A one-pass algorithm generally requires ''O''(''n'') (see [[Big O Notation|'big O' notation]]) time and less than ''O''(''n'') storage (typically ''O''(1)), where ''n'' is the size of the input.<ref name="eds"/> An example of a one-pass algorithm is the Sondik [[partially observable Markov decision process]].<ref name="pomdp"/>

==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 [[summation|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 ''n''th 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 [[mode (statistics)|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 algorithm|streaming algorithms]] but not one-pass algorithms.

== References==

<references>

<ref name="eds">{{Citation|last=Schweikardt|first=Nicole|title=One-Pass Algorithm|date=2009|url=https://doi.org/10.1007/978-0-387-39940-9_253|encyclopedia=Encyclopedia of Database Systems|pages=1948–1949|editor-last=LIU|editor-first=LING|editor-link=Ling Liu (computer scientist)|place=Boston, MA|publisher=Springer US|language=en|doi=10.1007/978-0-387-39940-9_253|isbn=978-0-387-39940-9|access-date=2021-04-13|editor2-last=ÖZSU|editor2-first=M. TAMER|url-access=subscription}}</ref>

<ref name="frankfurt">{{Cite web|last=Schweikardt|first=Nicole|title=One-Pass Algorithm|url=http://www.tks.informatik.uni-frankfurt.de/schweika/downloads/EncycDBS_OnePassAlgos.pdf|access-date=2021-07-01}}</ref>

<ref name="sjsu">{{Cite web|last=Pollett|first=Chris|date=2005-03-14|title=One and Two Pass Algorithms|url=http://www.cs.sjsu.edu/faculty/pollett/157b.12.05s/Lec14032005.pdf|access-date=2021-07-01}}</ref>

<ref name="pomdp">{{Cite web|url=http://www.pomdp.org/tutorial/sondik.html|title=Sondik's One-Pass Algorithm|website=www.pomdp.org}}</ref>

</references>

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[[Category:Streaming algorithms]]