We address the problem of expressing and evaluating computations on hierarchies represented as database tables. Engine support for such computations is very limited today, and so they are usually outsourced into stored procedures or client code. Recently, data model and SQL language extensions were proposed to conveniently represent and work with hierarchies. On that basis we introduce a concept of structural grouping to relational algebra, provide concise syntax to express a class of useful computations, and discuss algorithms to evaluate them efficiently by exploiting available indexing schemes. This extends the versatility of RDBMS towards a great many use cases dealing with hierarchical data.

Managing hierarchies is an ever-recurring challenge for relational database systems. Through investigations of customer scenarios at SAP we found that today's RDBMSs still leave a lot to be desired in order to meet the requirements of typical applications. Our research puts a new twist on handling hierarchies in SQL-based systems. We present an approach for modeling hierarchical data natively, and we extend the SQL language with expressive constructs for creating, manipulating, and querying a hierarchy. The constructs can be evaluated efficiently by leveraging existing indexing and query processing techniques. We demonstrate the feasibility of our concepts with initial measurements on a HANA-based prototype.

Maintaining and querying hierarchical data in a relational database system is an important task in many business applications. This task is especially challenging when considering dynamic use cases with a high rate of complex, possibly skewed structural updates. Labeling schemes are widely considered the indexing technique of choice for hierarchical data, and many different schemes have been proposed. However, they cannot handle dynamic use cases well due to various problems which we investigate in this paper. We therefore propose our dynamic Order Indexes , which offer competitive query performance, unprecedented update efficiency, and robustness for highly dynamic workloads.

The problem of generating a cost-minimal edit script between two trees has many important applications. However, finding such a cost-minimal script is computationally hard, thus the only methods that scale are approximate ones. Various approximate solutions have been proposed recently. However, most of them still show quadratic or worse runtime complexity in the tree size and thus do not scale well either. The only solutions with log-linear runtime complexity use simple matching algorithms that only find corresponding subtrees as long as these subtrees are equal. Consequently, such solutions are not robust at all, since small changes in the leaves which occur frequently can make all subtrees that contain the changed leaves unequal and thus prevent the matching of large portions of the trees. This problem could be avoided by searching for similar instead of equal subtrees but current similarity approaches are too costly and thus also show quadratic complexity. Hence, currently no robust log-linear method exists.

Main-memory database systems are emerging as the new backbone of business applications. Besides flat relational data representations also hierarchical ones are essential for these modern applications; therefore we devise a new indexing and versioning approach for hierarchies that is deeply integrated into the relational kernel.