Swarup Acharya Phillip B. Gibbons Viswanath Poosala Sridhar Ramaswamy Presented By Vinay Hoskere

1. Introduction 2. AQUA 3. Problem with joins 4. Join synopses 5. Allocation 6. Maintenance of join synopses 7. Experimental Evaluation

 Traditional query processing: Exact answers, minimize response time, maximize throughput  Data warehouses: full precision of exact answer not needed, less time, minimum number of accesses to base data.  Random Sampling techniques: generate approximate answers  Foreign keys joins: Large tables increase the size of base relation. Schemes for providing approximate join aggregates that rely on using random samples of base relations suffer from disadvantages

 Approximate query answering : Improves response time, avoids access to original database  Maintains smaller sized statistical summaries – “SYNOPSES”  Provides confidence bounds.  It has 3 components ◦ Statistics Collection ◦ Query Rewriting ◦ Maintenance.  It sits on top of a DBMS.

 Natural set of synopses would be random samples from each of the base relation ◦ Non Uniform Result Sample ◦ Small join result sizes  Using samples on base relations is not feasible.

 Naïve way - execute all possible join queries and collect samples  Join synopses - samples are taken from small set of distinguished joins  This scheme is for foreign key joins Model database schema as a graph  vertex - base relation  directed edge (u to v) – if u has at least one attribute which is foreign key in v

 There is a 1-1 correspondence between a tuple in a relation ‘r’ & a tuple in the output of any foreign key join involving ‘r’ & any of its descendants in the graph.  The subgraph of G on the ‘k’ nodes in any k-way foreign key join must be a connected subgraph with a single root node

 For each node u in G, corresponding to a relation r1, define J(u) to be the output of the maximum foreign key join r 1 xr 2 x..xr k with source r 1.  Let Su be a uniform random sample of r 1.  The join synopsis J(S u ) is the output of S u xr 2 xr3…..xr k.  J(S u ) is a uniform random sample of J(u) with |S u | tuples.  Thus we can extract from our synopsis a uniform random sample of the output of any k-way foreign key join.

 Optimal strategy for allocating the available space among the various join synopses when certain properties of the query work load are known.  Let ‘S’ be a set of queries with selects, aggregates, group by’s & foreign key joins.  For each relation R i, find fraction F i of queries in S for which R i is the source relation in a foreign key join.  The average relative error bound over the queries is proportional to sum(F i /sqrt(n i )).

 Heuristic allocation: When properties of work load are not known.  There are 3 procedures-  EqJoin – Divides up the space allotted equally amongst relations  CubeJoin – Divides up the space in proportion to the cube root of their join synopsis tuple size.  PropJoin – Divides up the space in proportion to their join synopsis tuple size.

 Need to maintain the join synopses when base relation is updated (insert or delete)  does not require frequent access to base relation  If a new tuple is inserted ◦ Let P u be the probability of newly arrived tuple for relation u in random sample S u ◦ Let uxr 2 xr 3 …..xr k be the max foreign key join with source u. ◦ We add ‘T’ (new tuple) to S u with probability P u. ◦ If ‘T’ is added to S u, we add to J(S u ) the tuple Txr 2 xr 3 …..xr k

◦ If T is added to S u and S u exceeds its target size, then select uniformly at random a tuple T’ to evict from S u and remove the tuple in J(S u ) corresponding to T’.  On delete of a tuple T from u ◦ T is in S u delete the tuple from S u and remove the tuple from J(S u ) corresponding to T ◦ If sample becomes too small due to many deletions repopulate by scanning relation u.  This algorithm performs lookups with the base relation with small probability P u

 Test bed – TPC-D decision support benchmark. DB of around 300 MB.  Machine – 296MHz UltraSPARC-II, 256 MB of memory, Solaris 5.6.  Query used is based on Q5 & an aggregate computed on join of Lineitem, Customer, Order, Supplier, Nation, Region.  The query used is

 Approximate query answering is becoming increasingly essential in data warehouses.  One of the fundamental problems faced here : computing approximate answers to aggregates on multi way joins.  Join synopses : Solution for schemas that involve foreign key joins.  Provides better performance than schemas based on base samples  Can be maintained efficiently during updates  Approximating answers for group by, rank and set valued queries still remains.