Minimal Indices for Successor Search

We give a new successor data structure which improves upon the index size of the Pǎtraşcu-Thorup data structures, reducing the index size from O(nw) bits to O(n logw) bits, with optimal probe complexity. Alternatively, our new data structure can be viewed as matching the space complexity of the (probe-suboptimal) z-fast trie of Belazzougui et al. Thus, we get the best of both approaches with respect to both probe count and index size. The penalty we pay is an extra O(logw) interregister operations. Our data structure can also be used to solve the weak prefix search problem, the index size of O(n logw) bits is known to be optimal for any such data structure. The technical contributions include highly efficient single word indices, with out-degree w/ logw (compared to the w out-degree of fusion tree based indices). To construct such high efficiency single word indices we device highly efficient bit selectors which, we believe, are of independent interest.