The controlled rounding problem: Complexity and computational experience

Controlled rounding is a procedure whereby tabular data gathered from respondents is perturbed in such a way as to preserve the anonymity of the respondents while maintaining the integrity of the data. Controlled rounding of two-dimensional tables can be represented by a straightforward network flow representation. Three-dimensional controlled rounding problems, on the other hand, have no pure network analog and have been shown to be NP-complete. A number of complexity results associated with the three-dimensional problem and its variants are discussed. In addition, the authors review several solution procedures for solving two- and three-dimensional problems. The algorithms reviewed are based on network flow models and linear programming techniques embedded within binary search procedures. The authors next turn to heuristics in order to reduce the running times of the solution procedures. Of these, simulated annealing is the most effective procedure for reducing the computational burden of the three-dimensional problem.