The design of distributed databases is an optimization problem requiring solutions to several interrelated problems: data fragmentation, allocation, and local optimization. Each problem can be solved with several different approaches thereby making the distributed database design a very difficult task. Although there is a large body of work on the design of data fragmentation, most of them are either ad hoc solutions or formal solutions for special cases (e. g., binary vertical partitioning). In this paper, we address the problem of n-ary vertical partitioning problem and derive an objective function that generalizes and subsumes earlier work. The objective function derived in this paper is being used for developing heuristic algorithms that can be shown to satisfy the objective function. The objective function is also being used for comparing previously proposed algorithms for vertical partitioning. We first derive an objective function that is suited to distributed transaction proces...

This paper presents new Lagrangian Heuristics for the set covering problem (SCP). These heuristics are designed to be embedded within an algorithm (e.g., subgradient optimization) to search for optimal Lagrangian multipliers. A Lagrangian heuristic may adjust a (perhaps infeasible) solution of a Lagrangian relaxation and/or make use of information available in the form of the Lagrangian multipliers. Such an algorithm was presented by J.E. Beasley who reported that, in computational experiments, it outperformed a number of other existing heuristic algorithms. However, his heuristic algorithm which uses only the Lagrangian relaxation solution and ignores the multipliers, worked well only for random-cost problems which may bear little resemblance to typical real world applications. We present four extensions of his algorithm designed to perform well for classes of problems which appear to be much harder to solve than Beasley's random-cost problems but which more adequately model real world problems, i.e., unicost and correlated-cost problems. (The latter class displays a positive correlation between the cost of a column and its density, i.e., the number of rows covered.) Computational results, based on problems involving 200 rows and 1000 columns, indicate that our Lagrangian heuristics do produce good-quality solutions and outperform Beasley's heuristic significantly for unicost and correlated-cost problems.