Bx-tree

Abstract: The Bx-tree [1] is a query and update efficient B+-tree11 based index structure for moving objects which are rep12 resented as linear functions. The Bx-tree uses a lineariza13 tion technique to exploit the volatility of the data values 14 being indexed i. e., moving-object locations. Specifically, 15 data values are first partitioned according to their update 16 time and then linearized within the partitions according 17 to a space-filling curve, e. g., the Peano or Hilbert curve. 18 The resulting values are combined with their time partition 19 information and then indexed by a single B+-tree. Figure 1 20 shows an example of the Bx-tree with the number of index 21 partitions equal to two within one maximum update inter22 val tmu. In this example, there are maximum of three 23 partitions existing at the same time. After linearization, 24 object locations inserted at time 0 are indexed in partition 25 1, object locations updated during time 0 to 0.5 tmu are 26 indexed in partition 2 and objects locations updated during 27 time 0.5 tmu to time tmu are indexed in partition 3 (as 28 indicated by arrows). As time elapses, repeatedly the first 29 range expires (shaded area), and a new range is appended 30 (dashed line). This use of rolling ranges enables the Bx31 tree to handle time effectively. 32