Space-Efficient B Trees via Load-Balancing.

We study succinct variants of B trees in the word RAM model that require s + o(s) bits of space, where s is the number of bits essentially needed for storing keys and possibly other satellite values. Assuming that elements are sorted by keys (not necessarily in the order of their integer representations), our B trees support standard operations such as searching, insertion and deletion of elements. In some applications it is useful to associate a satellite value to each element, and to support aggregate operations such as computing the sum of values, the minimum/maximum value in a given range, or search operations based on those values. We propose a B tree representation storing n elements in s + O( s/ lg n) bits of space and supporting all mentioned operations in O(lg n) time.