GDCRT: In-Memory 2D Geographical Dynamic Cascading Range Tree

Abstract

With the rapid increase of GPS users, the performance of location-based services (LBS) has gradually become a hot research topic. As the core algorithm of LBS, fast range query processing with massive data become the key problem. Till now, the main structures in this field are R-tree and its varieties. Although they can be adapted to a variety of dynamical data-set, and process insert/deletion in $O(\log n)$, there are still two essential defects when processing range query in it. Firstly, their time boundary for range query is $O(\sqrt{n})$. Secondly, their performance are based on heuristic algorithm. Given these two facts, the performance of R-trees is intolerable and unstable. Thus, in this paper, we introduce Geographical Dynamic Cascading Range Tree (GDCRT), a 2D dynamic index tree aiming at geographical range query in points data-set. The main innovation of GDCRT is to make fractional cascaded Range-tree dynamical by applying AVL-tree’s balance principle. For insertion and deletion, its time complexity is $O(\log n)$, which is equal to R-tree. For range query, its time boundary is $\theta (k+\log n)$, which is lower compared to R-tree series. And final experiment results also prove the correctness and efficiency of our structure.