1. Indexing Positions of Moving Objects Using B + -trees 4-th WIM meeting, Aalborg 2002 Laurynas Speičys laurynas@www.cs.auc.dk

2. 2 Outline B + -tree Expiration Times Space Filling Curves

3. 3 B + -tree Balanced search tree (all leafs are at the same level) Keys are ordered within a node A node has min. and max. bounds on the number of keys Figure: 4 levels k 1  k 2  k 3  … Bounds: min=5; max=10 … k1k1 k2k2 k3k3 … k1k1 k2k2 k3k3 k0k0 k0k0 knkn knkn

4. 4 Expiration Times Every update of the index requires a deletion and an insertion, i.e., two traversals of the tree d1d1 d2d2 d3d3

5. 5 Expiration Times d1d1 d2d2 d3d3 d1d1 d2d2 d3d3 Every update of the index requires a deletion and an insertion, i.e., two traversals of the tree

6. 6 Expiration Times d1d1 d2d2 d3d3 d1d1 d2d2 d3d3 Every update of the index requires a deletion and an insertion, i.e., two traversals of the tree “Expiration time” allows to avoid deletion traversals The index is more update- efficient

7. 7 Space Filling Curves Space filling curve can linearly order parts of n-dimensional space

8. 8 Implement, test, and improve algorithms for indexing positions of moving objects Ingredients: B + -trees Expiration times Space filling curves Proposal