We present incremental evaluation algorithms to compute changes to materialized views in relational and deductive database systems, in response to changes (insertions, deletions, and updates) to the relations. The view definitions can be in SQL or Datalog, and may use UNION, negation, aggregation ( e.g. SUM, MIN), linear recursion, and general recursion. We first present a counting algorithm that tracks the number of alternative derivations (counts) for each derived tuple in a view. The algorithm works with both set and duplicate semantics. We present the algorithm for nonrecursive views (with negation and aggregation), and show that the count for a tuple can be computed at little or no cost above the cost of deriving the tuple. The algorithm is optimal in that it computes exactly those view tuples that are inserted or deleted. Note that we store only the number of derivations, not the derivations themselves. We then present the Delete and Rederive algorithm, DRed, for incremental maintenance of recursive views (negation and aggregation are permitted). The algorithm works by first deleting a superset of the tuples that need to be deleted, and then rederiving some of them. The algorithm can also be used when the view definition is itself altered.

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Abstract.A data warehouse stores materialized views derived from one or more sources for the purpose of efficiently implementing decisionsupport or OLAP queries. One of the most important decisions in designing a data warehouse is the selection of materialized views to be maintained at the warehouse. The goal is to select an appropriate set of views that minimizes total query response time and/or the cost of maintaining the selected views, given a limited amount of resource such as materialization time, storage space, or total view maintenance time. In this article, we develop algorithms to select a set of views to materialize in a data warehouse in order to minimize the total query response time under the constraint of a given total view maintenance time. As the above maintenance-cost view-selection problem is extremely intractable, we tackle some special cases and design approximation algorithms. First, we design an approximation greedy algorithm for the maintenance-cost view-selection problem in OR view graphs, which arise in many practical applications, e.g., data cubes. We prove that the query benefit of the solution delivered by the proposed greedy heuristic is within 63% of that of the optimal solution. Second, we also design an A * heuristic, that delivers an optimal solution, for the general case of AND-OR view graphs. We implemented our algorithms and a performance study of the algorithms shows that the proposed greedy algorithm for OR view graphs almost always delivers an optimal solution.

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Data warehouses contain large amounts of information, often collected from a variety of independent sources. Decision-support functions in a warehouse, such as on-line analytical processing (OLAP), involve hundreds of complex aggregate queries over large volumes of data. It is not feasible to compute these queries by scanning the data sets each time. Warehouse applications therefore build a large number of summary tables , or materialized aggregate views, to help them increase the system performance. As changes, most notably new transactional data, are collected at the data sources, all summary tables at the warehouse that depend upon this data need to be updated. Usually, source changes are loaded into the warehouse at regular intervals, usually once a day, in a batch window, and the warehouse is made unavailable for querying while it is updated. Since the number of summary tables that need to be maintained is often large, a critical issue for data warehousing is how to maintain the summary tables efficiently. In this paper we propose a method of maintaining aggregate views (the summary-delta table method), and use it to solve two problems in maintaining summary tables in a warehouse: (1) how to efficiently maintain a summary table while minimizing the batch window needed for maintenance, and (2) how to maintain a large set of summary tables defined over the same base tables. While several papers have addressed the issues relating to choosing and materializing a set of summary tables, this is the first paper to address maintaining summary tables efficiently.