Supriya Ghosh (Editor)

One pass algorithm

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In computing, a one-pass algorithm is one 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.

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Basically one-pass algorithm operates as follows: (1) the object descriptions are processed serially; (2) the first object becomes the cluster representative of the first cluster; (3) each subsequent object is matched against all cluster representatives existing at its processing time; (4) a given object is assigned to one cluster (or more if overlap is allowed) according to some condition on the matching function; (5) when an object is assigned to a cluster the representative for that cluster is recomputed; (6) if an object fails a certain test it becomes the cluster representative of a new cluster

Example problems solvable by one-pass algorithms

Given any list as an input:

  • Count the number of elements.
  • Find the nth element (or report that the list has fewer than n elements).
  • Find the nth element from the end (or report that the list has fewer than n 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.

    • 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 middle element of the list.

    • Given a list of numbers:

  • Find the median.
  • Find the modes (This is not the same is finding the most frequent symbol from a limited alphabet).
  • Sort the list.

    • References

    One-pass algorithm Wikipedia
    (Text) CC BY-SA