Definition: (1) a structure providing an easily verified bound on the optimal value of an optimization problem. Typically used in the analysis of an approximation algorithm to prove the performance guarantee. (2) a mismatch of two symbols of string y at a distance of d is a "witness" to the fact that in no subject y could occur twice at a distance of exactly d positions (equivalently, that d cannot be a period of y).
See also certificate.
Note: From Algorithms and Theory of Computation Handbook, pages 13-17 and 34-18, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.
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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, "witness", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/witness.html