Controlled Randomized Rounding

A problem arising in statistics is the one of controlled rounding. Given a two-dimensional table, we want to round its entries in such a way that row and column sums are maintained (or atmost minimally changed). To prevent a bias, this is often realized as randomized rounding. Here (in addition to the table entries) we require the row and column sums to be randomized roundings as well. This make the problem a randomized rounding problem with hard constraints. Such problems recieved quite some attention recently, see e.g. [Sri01,GKPS02,Doe04,Doe06]. Controlled rounding is often used for confidentiality protection purposes. Frequency counts that directly or indirectly disclose small counts may permit the identification of individual respondents, which is of course undesirable. One way to prevent this is to round all numbers in the table to multiples of some integer b. This can be done with the rounding approach of [GKPS02] in time O(mn max{m,n}). We extend their method to exploit the fact the we round to multiples of an integer. In all resonable situations, this improves the run-time. If b is the product b = p1 . . . pr of primes p1, . . . , pr, our run-time is O(mn(p 2 1 + . . . + Electronic Notes in Discrete Mathematics 25 (2006) 39–40