1. Multi-dimensional Queries in P2P Systems

2. Applications Photo-sharing (photographs tagged with metadata) Multi-player online games (locate objects and other users)

3. System’s Components Partitioning Strategy (distribute data across nodes) Routing Strategy (transmit a query to the relevant nodes)

4. SCRAP: SPACE-FILLING CURVES WITH RANGE PARTITIONING

5. Partitioning Strategy Data are mapped into a single dimension e.g. (0100,0101) -> 01000101 Single-dimensional data are range- partitioned across a dynamic set of nodes

6. Routing Strategy Multi-dimensional range query is converted to a set of 1-d range queries Route each of 1-d range queries (Skip graph: A Chord-like connection between the nodes, which promises O(logn) messages)

7. Desiderata Locality: Nearby data points in the multi-dimensional space are also adjacent in the single dimension Load Balance: Management of neighboring ranges Node with empty partition splits the range of heavily loaded node

8. Desiderata Minimal metadata : Each node knows only partition boundaries of itself and its neighbors Low state : O(logn) links per node Routing load balance : Achieved due to the symmetric nature of skip graphs Query routing : O(logn) hops for each 1-d

9. Questions?