Two important problems related to multi-dimensional contingency tables are examined. The first is to compute exact integer bounds on internal entries given a set of marginal totals. This problem is central to preserving confidentiality in a statistical data base subject to public access queries. One important scenario requires the data administrator to determine a priori which data aggregates can and cannot be released. Interesting sets of releasable aggregates often include sufficient statistics for a Log-Linear model. The second problem is that of sampling from multi-dimensional contingency tables subject to a set of sufficient statistics (marginals). This problem arises from the need to determine exact tests of hypothesis in discrete multivariate analysis and recently has been approached using Markov Chain Monte Carlo methods. In general, both problems are extremely computationally demanding. We characterize those Log-Linear models that can be represented as mathematical networks. We demonstrate that this characterization includes all conditional independence models, but, in dimension k > 3, excludes all complete independence and no k-factor effects models in all but one important class of tables, namely, those of size rxcx2(superscript: k-2). For network models, the first problem is straightforward, and we provide an explicit, computationally efficient algorithm for the second. We also include an explicit, non-network, solution to the first problem for independence models. This is work in progress.