Efficient Dynamic Range Searching Using Data Replication

Given the lower bound of $\Omega(n^{(d-1)/d})$ for range query time complexity on $n$ $d$-dimensional point data, we investigate whether little replication can improve the query and update times significantly. We propose linear-space index structures that minimize the query and update times; the query time we achieve is $O(n^{\epsilon})$ for any $\epsilon <0$, and, the update time is $O(\log n)$.