(Submitted on 19 Jun 2008)
Abstract: This report details the generation and use of tree node ordering keys in a single relational database table. The keys for each node are calculated from the keys of its parent, in such a way that the sort order places every node in the tree before all of its descendants and after all siblings having a lower index. The calculation from parent keys to child keys is simple, and reversible in the sense that the keys of every ancestor of a node can be calculated from that node's keys without having to consult the database.Image may be NSFW.
Proofs of the above properties of the key encoding process and of its correspondence to a finite continued fraction form are provided.
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