Optimal implementation of selectors in a data-base

The records of a data base can be accessed from other records or from a set of data items (inverted access, primary and secondary index of IMS, search keys of CODASYL etc.) which we call selectors. The implementation of this selectors can use different techniques as hash coding, inverted lists or hierarchical index (indexed sequential, B-trees etc…) We consider here the last one and we search for a given set of selectors an optimal index structure. We show how this problem can be put as the search of an optimal rooted tree among the partial subgraphs of a given graph G (this problem is known in graph theory as Steiner problem) and we give several properties which allow the graph G to be notabily reduced. Then we present a branch and bound algorithm to solve this problem.