Algorithm 1: Real-Time Spatial Retrieval

Input: Query Q (MBR), DyGLIN Index

Output: Result Set R

1: $R_{\mathrm{final}}=\varnothing$

2: /* Index probe (top-level RMI probing) */

3: $\mathrm{LeafNodes}{L}_{\mathrm{set}}=\mathrm{Index}.\mathrm{RMI}\_\mathrm{Probe}(Q.Z_{\mathrm{interval}})$

4: for each $\mathrm{LeafNode}L\in L_{\mathrm{set}}$ do

5:    $C_{\mathrm{total}}=\varnothing$

6:    /* 1. HMBR filter */

7:    $C_{\mathrm{hmbr}}=\mathrm{L}.\mathrm{HMBR}.\mathrm{Query}(Q.\mathrm{MBR})$

8:    $C_{\mathrm{total}}.\mathrm{add}\left(C_{\mathrm{hmbr}}\right)$

9:    /* 2. Incremental buffer filter */

10:    $C_{\mathrm{db}}=\mathrm{L}.\mathrm{DB}.\mathrm{Scan}(Q.\mathrm{MBR})$

11:    $C_{\mathrm{total}}.\mathrm{add}\left(C_{\mathrm{db}}\right)$

12:    /* 3. CF filter */

13:    $C_{\mathrm{filtered}}=\varnothing$

14:    for each $\mathrm{Payload}P\in C_{\mathrm{total}}$ do

15:       if $\mathrm{L}.\mathrm{CF}.\mathrm{Contains}(P.\mathrm{ID})=\mathrm{false}$ then

16:       $C_{\mathrm{filtered}}.\mathrm{add}\left(P\right)$

17:       end if

18:    end for

19:    /* 4. Final refinement */

20:    $R_{\mathrm{refined}}=\mathrm{Refine}(C_{\mathrm{filtered}},Q.\mathrm{Geometry})$

21:    $R_{\mathrm{final}}.\mathrm{add}\left(R_{\mathrm{refined}}\right)$

22: end for

23: return $R_{\mathrm{final}}$