(definition)

**Definition:**
A searching problem for which one can decompose the searched domain into subsets, find answers from these subsets, and combine these answers to form the solution to the original problem. More formally a problem with a query Q is decomposable given if there exists an efficiently computable *associative* and *commutative* binary operator @ satisfying the condition: Q(x, A ∪ B) = @(Q(x,A),Q(x,B)).

*Note:
From Algorithms and Theory of Computation Handbook, page 20-26, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.*

Author: CRC-A

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Entry modified 17 December 2004.

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Cite this as:

Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "decomposable searching problem", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/decomposable.html