ALCOMFT-TR-03-108

P. Jonsson and A. Krokhin
Computational complexity of auditing finite attributes in statistical databases
Warwick. Work packages 1 and 4. November 2003.

Abstract: We study the computational complexity of auditing finite attributes in databases allowing statistical queries. Given a database that supports statistical queries, the auditing problem is to check whether an attribute can be completely determined or not from a given set of statistical information. Some restricted cases of this problem have been investigated earlier, e.g. the complexity of statistical sum queries is known by the work of Kleinberg et al. (J. CSS 66 (2003) 244-253). We characterise all classes of statistical queries such that the auditing problem is polynomial-time solvable. We also prove that the problem is coNP-complete in all other cases under a plausible conjecture on the complexity of constraint satisfaction problems. This result is obtained by exploiting connections between auditing and constraint satisfaction, and using certain algebraic techniques. We also study a generalisation of the auditing problem where one asks if a set of statistical information imply that an attribute is restricted to K or less different values. We characterise all classes of polynomial-time solvable problems also in this case.

Postscript file: ALCOMFT-TR-03-108.ps.gz (141 kb).