An important problem in the physical design of databases is the selection of secondary indices. In general, this problem can not be solved in an optimal way due to the complexity of the selection process. Often use is made of heuristics such as the well-known ADD and DROP algorithms. In this paper it will be shown that frequently used cost functions can be classified as super- or submodular functions. For these functions several mathematical properties have been derived which reduce the complexity of the index selection problem. These properties will be used to develop a tool for physical database design and also give a mathematical foundation for the success of the before-mentioned ADD and DROP algorithms. Keywords: Physical database design, Secondary index selection, ADD and DROP algorithms, Supermodular functions, Submodular functions. 1 Introduction Physical database design is an important step in designing databases and aims to generate efficient storage structures for the data....

We present a conceptual framework in which a database’s intra- and interrecord set access require-ments are specified as a constrained assignment of abstract characteristics (“evaluated, ” “indexed,” “clustered, ” ‘I well-placed”) to logical access paths. We derive a physical schema by choosing an available storage structure that most closely provides the desired access characteristics. We use explicit replication of schema objects to reduce the access cost along certain paths, and analyze the trade-offs between increased update overhead and improved retrieval access. Finally, we give an algorithm to select storage structures for a CODASYL 78 DBTG schema, given its access requirements specification.

this paper can be found in section 2.2.

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