Effects of Updates On Optimality In Tries and Doubly-Chained Trees CS TR-256

The doubly-chained tree is a data structure for organizing files in a database system. We model such systems with a trie, a tree in which leaves correspond to records from a file. Retrieval proceeds by following a path in a trie from the root to a leaf, where the edge taken at each node is determined by some attribute value of the query. For a given file, altering the order in which attributes are tested can change the size of the resulting trie; tries with minimum size are considered optimum. We explore the preservation of optimality under the operations of inserting a record into the file, deleting a record from the file, and deleting any record from the file, showing that even for binary files a single update may be sufficient to make all optimum tries nonoptimum. The same results hold when the criterion of optimality is the average access time of a leaf. Finding an indexing set for a file consists of finding a subset of the attributes which distinguish all records. We show that there are files for which a single insertion or deletion may make a minimum indexing set invalid so that no superset or subset, respectively, can be a minimum indexing set for the new file.