Indexing Data Relationships Michael J. Franklin University of California, Berkeley & RightOrder Inc.

2 Overview Data relationships can be complex. Hierarchical views: XML, LDAP, … Semistructure & dynamic schema Approach:Encode paths as tagged strings “raw” paths encode structure “refined” paths accelerate lookups Index strings in a highly-compact structure. Live on top of, next to or inside DBMS. Benefits Performance, Scalability + Adaptivity Leverages mature DBMS technology

3 Raw paths w/Designators  ABC Corp.  123 ABC Way  17 Main St.  Goods Inc.  widget  thingy  jobber Invoice as a tree Invoice Buyer Seller Itemlist Name Address Item ABC Corp.123 ABC Way Goods Inc. 17 Main St. widgetthingyjobber Name Address Item           

4 Refined paths Optimize specific access paths “Find invoices where X sold to Y ” “Find invoices where X bought Y and Z” “Find invoices where a buyer bought X, Y and Z ”  X Y  ABC Corp. Goods Inc.  XYZ Corp. Acme Inc.  ABC Corp. jobber widget  XYZ Corp. drill hammer  X Y Z  X Y Z  jobber thingy widget  drill hammer nail

5 Index Fabric An index structure for long strings. Provides fast lookups Handles long strings Ideal substrate for designated keys Based on Patricia tries Highly compressed string representation Cost in index independent of string length But, need to balance.

6 Patricia tries Indexes first point of difference between keys greenbeans greentea gc r w 0 22 corn cow a 2 grass 5 e b t greenbeansgreentea D. R. Morrison. “PATRICIA – Practical algorithm to retrieve information coded in alphanumeric.” J. ACM, 15 (1968) pp

7 Multiple Hierarchical Views Can store multiple permulations of relationships Find animals and the plants they eat Find plants and the animals that eat them Represent as a new set of keys Store data once using “permutation records”  corn  cow  corn  cow

8 Example  0 2 o a  cat 4  5 c  cow  corn 1  w 5 c  wheat  corn 6  c  cow

9 Example  0 2 o a  cat 4  5  corn 1  w 5 c  wheat 6   cow   cc

10 Balancing Patricia tries gc r w 0 22 corn cow a 2 grass 5 e b t greenbeansgreentea

11 Balancing Patricia tries Step 1: divide trie into blocks gc r w 0 22 corn cow a 2 grass 5 e b t greenbeansgreentea

12 Balancing Patricia tries Step 2: build another layer g 0 2 Layer 1 Layer 0 e gc r w 0 22 corn cow a 2 grass 5 e b t greenbeansgreentea

13 Balancing Patricia tries Search for “cash” g 0 2 Layer 1 Layer 0 e greenbeans gc r w 0 22 corn cow a 2 grass 5 e b t greenbeansgreentea

14 Balancing Patricia tries Search for “cash” g 0 2 Layer 1 Layer 0 e greenbeans gc r w 0 22 corn cow a 2 grass 5 e b t greenbeansgreentea

15 Balancing Patricia tries Search for “cash” g 0 2 Layer 1 Layer 0 e greenbeans gc r w 0 22 corn cow a 2 grass 5 e b t greenbeansgreentea

16 Balancing Patricia tries Layer 0 Data Search Layer 0 Layer 1 Layer 2 Layer 3

17 Performance Number of layers is small Fixed (small) space per key  High branching factor per block  Bushy, shallow tree Example: 8 KB blocks 32 bit pointers + 2 bytes for keys/structure = pointers per block = 3 layers for 1 billion pointers to data ( ) Upper layers are tiny (10 megabytes), in RAM Only layer 0 on disk  Usually one index I/O per key lookup Data

18 Find publications by co-authors RDBMS STORED 2.5 : 1 Index Fabric Raw Paths 5 : 1 Index Fabric Refined Paths 25 : 1 RDBMS Edge mapping 10,000 queries

19 Find publications by co-authors RDBMS STORED Index Fabric Raw Paths Index Fabric Refined Paths RDBMS Edge mapping 2.1 : 1 4 : 1 20 : 1 10,000 queries

20 Conclusion Index arbitrary relationships Encode as designated strings Relationships and structures can be complex Index many data access paths No need for DTD or pre-defined schema Index Fabric Special data structure for long keys High performance key lookups Supports designator encoding

21 For more information