1. Optimization of Sequence Queries in Database Systems Reza Sadri Carlo Zaniolo reza@cs.ucla.edu zaniolo@cs.ucla.edu sadri@procom.com Amir Zarkesh Jafar Adibi azarkesh@u4cast.com jabibi@u4cast.com

2. Time series Analysis Many Applications: Querying purchase patterns for marketing Stock market analysis Studying meteorological data What’s needed: Expressive query language for finding complex patterns in database sequences Effcient and scalable implementation: Query Optimization

3. State of The Art ADT (e.g.. Informix Datablades): Not flexible enough, no Optimization SEQ: Enhanced ADTs (e. g. sets and sequences) with their own query language SRQL: Adding sequence algebra operators to relational model

4. SQL-TS A query language for finding complex patterns in sequences Minimal extension of SQL—only the from clause affected A new Query optimization techniqe based on extensions of the Knuth, Morris & Pratt (KMP) string-search algorithm

5. SQL-TS: Example Having a table quote (name, date, price) of stock prices, find all the stocks that went up by 15% or more one day and went down by 20% or more the next day and retrieve the change in the value of the stock. SELECT X.name, (Z.price -X.price) AS price_change, X.date AS date FROM quote CLUSTER BY name SEQUENCE BY date AS (X, Y, Z) WHERE Y.price > 1.15 * X.price AND Z.price < 0.8 * Y.price

6. SQL-TS: Example Data sorted in each groupgrouped but not sorted

7. Optimized string search:KMP Consider text array text and pattern array p: i 1 2 3 4 5 6 7 8 9 10 11 text[i] a b a b a b c a b c a j 1 2 3 4 5 6 pattern[j] a b a b c a  After failing, use the information acquired so to: - backtrack to shift(j), rather than i+1, and - only check pattern values after next(j) But in SQL-TS we have general predicates & star patterns

8. Equality predicates: KMP Find companies whose closing stock price in three consecutive days was 10, 11, and 15. SELECT X.name FROM quote CLUSTER BY name SEQUENCE BY date AS (X, Y, Z) WHERE X.price =10 AND Y.price=11 AND Z.price=15

9. shift and next Success for first j-1 elements of pattern. Failure for jth element (when input is at i) Any shift less than shift(j) is guaranteed to lead to failure, Match elements in the pattern starting at next(j) Shifted Pattern i – j + 1 1 1 i – j + shift(j) + 1i - j + shift(j) + next(j) shift(j) + 1shift(j) + next(j) i j next(j)j - shift(j) Input Pattern shift(j)

10. Optimal Pattern Search (OPS) Search path for naive algorithm vs optimized algorithm:

11. Matrices  and  : Input tested on p j is now tested against p k Combing values of these lower triangular matrices ( j  k), We derive the values of next(j) and shift (j) p j succeeded: p j failed:

12. STAR Patterns SELECT X.NEXT.date, X.NEXT.price, S.previous.date, S.previous.price FROM quote CLUSTER BY name, SEQUENCE BY date AS (*X, Y, *Z, *T, U, *V, S) WHERE X.name='IBM‘ AND X.price > X.previous.price AND 30 < Y.price AND Y.price < 40 AND Z.price T.previous.price AND 35 < U.price AND U.price < 40 AND V.price < V.previous.price AND S.price < 30

13. Same input, Transitions on Original Pattern vs. Transitions on Pattern after the index set back j-k  21   31   32   41   42   43  Example: Elements j and k are star predicates and  jk is U: U   j,k+1   j+1,k  j+1,k+1 Handling Star Patterns

14. Possible Transitions from  jk p j is starp j is not star p k is star Diagonal and down,and if  jk is U, right Diagonal and down p k is not star Diagonal and right Only diagonal

15. Implication Graph

16. *Z (less than 2% change) *U (less than 2% change) *W (less than 2% change) *Y*R *V *T FSM Simulation used to Optimize Star Patterns Relaxed Double Bottom: Only considering increases and decreases that are more than 2%

17. Relaxed Double Bottom: Ninty fold improvement

18. Conclusions Disjunctive queries, partial ordered domains, aggregates also treated in this approach Old applications—more power & flexibility than Datablades ADTs of commercial DBMSs Ongoing implementation, by building on the user-defined aggregates supported in AXL.