One-pass algorithm
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In computing, a one-pass algorithm is a streaming algorithm which reads its input exactly once, in order, without unbounded buffering. 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.
Basically one-pass algorithm operates as follows:
- The object descriptions are processed serially
- The first object becomes the cluster representative of the first cluster
- Each subsequent object is matched against all cluster representatives existing at its processing time
- A given object is assigned to one cluster (or more if overlap is allowed) according to some condition on the matching function
- When an object is assigned to a cluster the representative for that cluster is recomputed
- If an object fails a certain test it becomes the cluster representative of a new cluster nothing happened
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. 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 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.
Given a list of numbers: