1. A Semantic Caching Method Based on Linear Constraints Yoshiharu Ishikawa and Hiroyuki Kitagawa University of Tsukuba {ishikawa,kitagawa}@is.tsukuba.ac.jp

2. Outline _ Background –Data caching –Semantic caching _ Our Approach _ Algorithms _ Future work and conclusion

3. Data Caching (1) _ Stores a query result into local cache _ Uses cached results for later queries: improves response time _ Based on the notion of temporal locality _ Used in various situations: –Client-server database environments –Data warehousing –has relationship with materialized view

4. Data Caching (2) Database Server DBMS Client Module Query Result Local Cache

5. Data Caching (3) Database Server DBMS Client Module Query Reminder Query Result Local Cache Information Examination Probe Query Result

6. Semantic Caching (1) _ Based on semantic locality (in addition to temporal locality) –Similar objects tend to be referenced together _ Related work –Semantic caching based on rectlinear region (Dar, Franklin, Srivastava et al.) –Predicate caching (Keller and Basu) –View caching (Roussopoulos et al.)

7. Semantic Caching (2) _ Semantic caching based on rectlinear region age salary Q1: SELECT * FROM Employee WHERE age  30 AND age  40 AND salary  2000 AND salary  3000 3040 3000 2000 Q2: SELECT * FROM Employee WHERE age  35 AND age  50 AND salary  2500 AND salary  4000 4000 50 stored into local cache

8. Semantic Caching (2) _ Semantic caching based on rectlinear region age salary Q1: SELECT * FROM Employee WHERE age  30 AND age  40 AND salary  2000 AND salary  3000 3040 3000 2000 Q2: SELECT * FROM Employee WHERE age  35 AND age  50 AND salary  2500 AND salary  4000 4000 50 probe query reminder query

9. Semantic Caching (3) age salary Probe Query SELECT * FROM Employee WHERE age  35 AND age  40 AND salary  2500 AND salary  3000 3040 3000 2000 Reminder Query SELECT * FROM Employee WHERE (age  35 AND age  40 AND salary  3000 AND salary  4000) OR (age  40 AND age  50 AND salary  2500 AND salary  4000) OR (age  40 AND age  50 AND salary  3000 AND salary  4000) 4000 50 probe query reminder query

10. Outline _ Background _ Our Approach –An example –Constraint data model _ Algorithms _ Future work and conclusion

11. Our Approach _ A new approach to semantic caching –Generalization of rectlinear region-based approach –Based on linear constraints _ Assumption: a query condition is a conjunction of (in)equality formulas _ Caches retrieved base tuples _ Maintains compact constraint relations to describe cached base tuples

12. An Example (1) Q1 SELECT name, year FROM UsedCar WHERE displacement  1500 AND price  8000 q 1 (displacement  1500)  (price  8000) client retieves all base tuples which satisfy q 1

13. An Example (1) Q1 SELECT name, year FROM UsedCar WHERE displacement  1500 AND price  8000 q 1 (displacement  1500)  (price  8000) client retieves all base tuples which satisfy q 1 cache-info client stores a tuple in cache-info to describe obtained tuples

14. An Example (2) Q2 SELECT name, price, tax FROM UsedCar WHERE displacement  1200 AND price + tax  10000 q 2 (displacement  1200)  (price + tax  10000) cache-info client examines cache-info to check the availability of tuples

15. An Example (3) Probe Query q 1  q 2 = ((displacement  1500)  (price  8000))  ((displacement  1200)  (price + tax  10000)) = (displacement  1500)  (price  8000)  (price + tax  10000) 8000 price tax

16. An Example (3) Probe Query q 1  q 2 = ((displacement  1500)  (price  8000))  ((displacement  1200)  (price + tax  10000)) = (displacement  1500)  (price  8000)  (price + tax  10000) 10000 8000 price tax

17. An Example (3) Probe Query q 1  q 2 = ((displacement  1500)  (price  8000))  ((displacement  1200)  (price + tax  10000)) = (displacement  1500)  (price  8000)  (price + tax  10000) 10000 8000 price tax semantic region for the probe query

18. An Example (4) Probe Query q 1  q 2 = (displacement  1500)  (price  8000)  (price + tax  10000) Reminder Query  q 1  q 2 = ((displacement 8000))  ((displacement  1200)  (price + tax  10000)) cache-info

19. Constraint Data Model _ Incorporates the notion of constraints directly into the data model _ Can represent infinite information in terms of finite representation _ A constraint data model is a combination of –Base data model: relational data model, datalog, etc. –Constraint domain: dense order, linear arithmetic, polynomials, etc.

20. Definition of the Data Model _ Constraint k-tuple  =  1 ...   N –  i : constraint (equality or inequality constraint) –In our case, linear constraints are used _ Linear constraint a 1 x 1 +... + a p x p  a 0 –a i : integer –   {=, ,,  } _ Constraint relation r = {  1,...,  M } –  i : constraint k-tuple –Also represented as r =  1 ...   M (disjunctive normal form)

21. Orthographic Partitioning _ Proposed by Grumbach et al. _ Partitions a constraint tuple into independent components _ Reduces computational complexity

22. Outline _ Background _ Our Approach _ Algorithms –Cache examination –Overlap computation –Cache replacement _ Future work and conclusion

23. Cache Examination Algorithm _ Checks the availability of cached base tuples _ Generates a probe query and a reminder query _ Takes orthographic partitioning into consideration t1t1 t2t2 q

24. Cache Examination Algorithm(1) _ Checks the availability of cached base tuples _ Generates a probe query and a reminder query _ Takes orthographic partitioning into consideration t1t1 t2t2 q probe query reminder query

25. Cache Examination Algorithm(2) _ The brief idea –For each tuple i in cache-info, compute pq i, its overlap with query q –The probe query is generated as pq := pq 1 ...  pq n –The reminder query is generated as rq := q   pq

26. Overlap Computation _ Requirement: delete redundant constraints from the overlap –e.g. (age > 30)  (age  50)  (age > 40) (age > 40)  (age  50) _ For this purpose, we applied a technique found in linear programming –Calculate all of the basic feasible solutions from the given constraints –If a solution does not exist, there is no overlap. –Resulting constraint is easily calculated

27. Cache Replacement _ A simple reference count-based algorithm –Sets a counter for each base tuple –If cache is full, it uses select-victim() function to select victims for the replacement (definition of the select-victim function is the future work). –If a reference counter becomes 0, its corresponding base tuple is deleted from the cache.

28. Outline _ Background _ Our Approach _ Algorithms –Cache examination –Overlap computation –Cache replacement _ Future work and conclusion

29. Future Work _ Efficient calculation of overlaps –Use of indexes –Minimum bounding box (MBB)-based approach _ Cache Replacement algorithm –Efficient replacement algorithm _ Simulation-based Evaluation

30. Conclusion _ A new approach to semantic caching –linear constraint-based approach _ A naive algorithm to compute a probe query and a reminder query –Overlap computation is the key factor –An overlap computation algorithm based on linear programming _ Proposal of replacement algorithm