Swarup Acharya Phillip B. Gibbons Viswanath Poosala Sridhar Ramaswamy

Presented By Vinay Hoskere

Join Synopses for Approximate Query Answering

1. Introduction2. AQUA3. Problem with joins4. Join synopses5. Allocation6. Maintenance of join synopses7. Experimental Evaluation

Contents

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

Introduction

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.

AQUA

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.

Problem with Joins

Join Synopses 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

Definition

Join Synopses 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

Definition

Join Synopses For each node u in G, corresponding to a relation

r1, define J(u) to be the output of the maximum foreign key join r1xr2x..xrk with source r1.

Let Su be a uniform random sample of r1. The join synopsis J(Su) is the output of

Suxr2xr3…..xrk. J(Su) is a uniform random sample of J(u) with |Su|

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 Ri, find fraction Fi of queries in S for which Ri is the source relation in a foreign key join.

The average relative error bound over the queries is proportional to sum(Fi /sqrt(ni)).

Allocation

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.

Allocation

Maintenance of Join Synopses 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 Pu be the probability of newly arrived tuple for relation u in random sample Su

◦ Let uxr2xr3…..xrk be the max foreign key join with source u.

◦ We add ‘T’ (new tuple) to Su with probability Pu.◦ If ‘T’ is added to Su, we add to J(Su) the tuple

Txr2xr3…..xrk

Maintenance of Join Synopses

◦ If T is added to Su and Su exceeds its target size, then select uniformly at random a tuple T’ to evict from Su and remove the tuple in J(Su) corresponding to T’.

On delete of a tuple T from u◦ T is in Su delete the tuple from Su and remove

the tuple from J(Su) 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 Pu

Experimental Evaluation 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

Experimental Evaluation

Experimental Evaluation

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.

Conclusion

Thank You.