Perspective Reformulations of the CTA Problem with L2 Distances

Any institution that disseminates data in aggregated form has the duty to ensure that individual confidential information is not disclosed, either by not releasing data or by perturbing the released data while maintaining data utility. Controlled tabular adjustment (CTA) is a promising technique of the second type where a protected table that is close to the original one in some chosen distance is constructed. The choice of the specific distance shows a trade-off: although the Euclidean distance has been shown (and is confirmed here) to produce tables with greater "utility," it gives rise to mixed integer quadratic problems (MIQPs) with pairs of linked semi-continuous variables that are more difficult to solve than the mixed integer linear problems corresponding to linear norms. We provide a novel analysis of perspective reformulations (PRs) for this special structure; in particular, we devise a projected PR (P2R), which is piecewise-conic but simplifies to a (nonseparable) MIQP when the instance is symmetric. We then compare different formulations of the CTA problem, showing that the ones based on P2R most often obtain better computational results.