RankSQL: Query Algebra and Optimization for Relational Top-k Queries AUTHORS: Chengkai Li Kevin Chen-Chuan Chang Ihab F. Ilyas Sumin Song Presenter: Roman Yarovoy October 3, 2007 1 Before RankSQL Ranking (top-k) queries: Query result is sorted by rank and limited to top k results. Support for ranking was lacking from RDBMS. Previously, isolated cases of top-k query processing were studied. No way to integrate top-k operations with other relational operations. 2 Previous (traditional) approach

Query processing without ranking support: 1. Evaluate select-project-join (SPJ) query and materialize the result. 2. Sort the result according to a given ranking function. 3. Take only top k tuples. Associated problems: No interest in total order of all the results. Evaluating ranking function(s) can be expensive. 3 Key contribution Li et al. proposed: Extending relational algebra to support ranking as a first-class database construct. Consequence: Rank-aware relational query engine Rank-aware query optimization. 4

Top-k query: Example 1 R T TID a1 a2 p1 p2 p3 TID b1 b2 p4 p5 r1

27 50 0.5 0.3 0.25 t1 47 55 0.5 0.1 r2 17 60 0.6

0.5 0.65 t2 66 65 0.5 0.7 r3 47 90 0.7 0.7 0.95 t3 27

15 0.5 0.8 r4 87 10 0.8 0.1 0.35 t4 99 95 0.5 0.2

r5 47 70 0.9 0.1 0.75 5 Example 1 (contd) SELECT * FROM R r, T t WHERE r.a1=t.b1 AND r.a2>t.b2 ORDER-BY p1+p2+p3+p4+p5 LIMIT 2 TID a1 a2 b1 b2

F r3/t1 47 90 47 55 2.95 r1/t3 27 50 27 15 2.35 r5/t1

47 70 47 55 2.35 (where F = p1+p2+p3+p4+p5) 6 Rank-relational algebra There was no way to express such query in relational algebra. Extend relational algebra by adding rank as a first-class operation. Based on the observations of first-class constructs (eg. selection), two requirements are needed to support ranking: 1. 2.

Splitting Predicate-by-predicate rank evaluation. Interleaving Swapping rank operator with other operators (i.e. ranking is not only applied after filtering). 7 Ranking Principle Def: Given a ranking function F and a set of evaluated predicates P={p1, p2, , pn}, maximal-possible score of a tuple t is defined as: Ranking Principle: If FP[t1] > FP[t2], then t1 must be ranked before t2. 8 Rank-Relation Def: For monotonic scoring function F(p1, , pn) and a subset P of {p1, , pn}, a relation R augmented with ranking induced by P is called a rank-relation, denoted by RP. Implicit attribute of RP is the score of tuple t, that is FP[t]. Order relationship of RP : For all t1, t2 RP : t1 < RP t2 FP[t1] < FP[t2] 9 Operators of rank-relations Rank (or ) operator adds a predicate p to set P. i.e.

p(RP) R P U{p}. Example 2: p1(R{p2}) R{p1, p2}, where F=(p1, p2, p3). TID a1 a2 p1 p2 p3 r3 47 90 0.7 0.7

0.95 2.4 r2 17 60 0.6 0.5 0.65 2.1 r5 47 70 0.9 0.1 0.75

2.0 r4 87 10 0.8 0.1 0.35 1.9 r1 27 50 0.5 0.3 0.25

1.8 F{p1, p2} 10 Extended operators 11 Example 3: Extended Join a1,a2,b2(c (R{p1, p2 p3} JOIN T{p4, p5})) SELECT r.a1, r.a2, t.b1 FROM R r, T t WHERE c ORDER-BY F LIMIT 2 TID a1 a2 b2 F {p1, p2, p3, p4, p5}

r2/t4 17 60 99 2.45 r4/t4 87 10 99 1.95 r1/t4 27 50 99 1.75 (F = P and c = r.a1+r.a2 < t.b1) 12 Extended operators (contd) Note: Cartesian product is defined similarly to join, but not discussed in the paper. Projection operator has not changed. Computation is based on both Boolean and ranking logical properties. Perform Boolean operations and maintain the order induced by all given ranking predicates. 13 Equivalence relations

In the extended rank-relational model, ranking is a firstclass construct. Can derive algebraic equivalences from the definitions of operators (Proofs are omitted). Example 4: 1. c(RP) (cR)P 2. RP1 TP2 (R T)P1 U P2 Thus, we can interleave the rank operator with other operators (i.e. push down across operators). 14 Equivalence relations (contd) 15 Equivalence relations (contd) Note: Proposition 1 states that ranking can be done in stages (i.e. one predicate at the time). By Propositions 2, 3, and 4, the relations hold commutative and associative laws. By Propositions 4 and 5, can be swapped with other operators.

16 Incremental execution Blocking operators (eg. sort) lead to materialization of intermediate results. Goal: To avoid materialization and implement a pipelining execution strategy. We want to split rank computation into stages and to reduce the number of tuples considered in the upcoming stages. We can output (i.e. advance to the next stage) a tuple t, whenever t has a score which is greater or equal to the score of any future tuple t . 17 Incremental execution (contd) Apply p to RP and maintain priority queue ordered by P U{p}. Let X = set of tuples from preceding stage. Draw t from X. If FP U{p}[t] FP[t] and future t drawn from x, FP[t] FP[t] for any

then FP U{p}[t] FP U{p}[t] and t can be output (proceed to next stage). 18 Example 5: Top 2 of W Given F = AVG(p6, p7, p8) idxScanp6(W) TID x p6 p7 p8 F p7 p8 TID x F TID x F

w1 3 0.9 0.8 0.2 29/30 w1 3 9/10 w1 3 19/30 w2 7 0.8

0.7 0.1 14/15 w2 7 5/6 w4 1 3/5 5 0.7 0.6 0.1 5

w2 7 8/15 w3 w3 23/30 9/10 w4 1 19/30 w3 5 7/15 w4 1

0.5 0.4 0.9 5/6 19 Different evaluation plans There exist algorithms to implement rank-aware operators as well as incremental evaluation. Efficiency of query evaluation will now depend not only on the regular operators, but also on the rankaware operators. Due to algebraic equivalence laws, we can define additional evaluation plans. Hence, we want a query optimizer to take additional execution plans into consideration. 20 Rank-aware optimizer Extended algebra Extended search space. Impact on enumeration algorithm: Li et al. designed a 2-dimension enumeration algorithm: Dimension 1 = Join size, Dimension 2 = Ranking predicates. The algorithm is exponential in both dimensions.

Heuristics applied to reduce search space. Impact on cost model: For ranking queries, it is more difficult to estimate the query cardinality of the intermediate results, whose accuracy is the core of the cost model. Authors proposed to estimate cardinality by randomly sampling tuples. 21 Critique Erroneous examples. No example of tie-breaking function. Bad explanation of incremental evaluation. 22 Future research directions Cardinality estimation: New/improved techniques for random sampling over joins. Dynamically determined/chosen k. Exploring physical properties of rank-aware execution plans. 23