Exact and approximate algorithms for the index selection problem in physical database design

The index selection problem (ISP) is an important optimization problem in the physical design of databases. The aim of this paper is to show that ISP, although NP-hard, can in practice be solved effectively through well-designed algorithms. We formulate ISP as a 0-1 integer linear program and describe an exact branch-and-bound algorithm based on the linear programming relaxation of the model. The performance of the algorithm is enhanced by means of procedures to reduce the size of the candidate index set. We also describe heuristic algorithms based on the solution of a suitably defined knapsack subproblem and on Lagrangian decomposition. Finally, computational results on several classes of test problems are given. We report the exact solution of large-scale ISP instances involving several hundred indexes and queries. We also evaluate one of the heuristic algorithms we propose on very large-scale instances involving several thousand indexes and queries and show that it consistently produces very tight approximate (and sometimes provably optimal) solutions. Finally, we discuss possible extensions and future directions of research.