Nested set model

The nested set model is a particular technique for representing nested sets (also known as trees or hierarchies) in relational databases. The term was apparently introduced by Joe Celko; others describe the same technique using different terms.

The technique is an answer to the problem that the standard relational algebra and relational calculus, and the SQL operations based on them, are unable to express all desirable operations on hierarchies directly. A hierarchy can be expressed in terms of a parent-child relation - Celko calls this the adjacency list model - but if it can have arbitrary depth, this does not allow the expression of operations such as comparing the contents of hierarchies of two elements, or determining whether an element is somewhere in the subhierarchy of another element. When the hierarchy is of fixed or bounded depth, the operations are possible, but expensive, due to the necessity of performing one relational join per level. This is often known as the bill of materials problem.

Hierarchies may be expressed easily by switching to a graph database. Alternatively, several resolutions exist for the relational model and are available as a workaround in some relational database management systems:

When these solutions are not available or not feasible, another approach must be taken.

The nested set model is to number the nodes according to a tree traversal, which visits each node twice, assigning numbers in the order of visiting, and at both visits. This leaves two numbers for each node, which are stored as two attributes. Querying becomes inexpensive: hierarchy membership can be tested by comparing these numbers. Updating requires renumbering and is therefore expensive. Refinements that use rational numbers instead of integers can avoid renumbering, and so are faster to update, although much more complicated.

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