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DBMS Overview
• DBMSs
• Query Evaluation
• Mapping SQL to RA
• Mapping Example
• Query Cost Estimation
• Implementations of RA Ops
• DBMS Architecture
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❖ DBMSs
DBMS = DataBase Management System
Our view of the DBMS so far …

A machine to process SQL queries.
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❖ DBMSs (cont)
One view of DB engine: “relational algebra virtual machine”
Machine code for such a machine:
selection (σ)
projection (π)
join (⨝, ×)
union (∪)
intersection (∩)
difference (-)
sort
insert
delete
For each of these operations:
• various data structures and algorithms are available
• DBMSs may provide only one, or may provide a choice
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❖ Query Evaluation
The path of a query through its evaluation:

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❖ Mapping SQL to RA
Mapping SQL to relational algebra, e.g.
— schema: R(a,b) S(c,d)
select a as x
from R join S on (b=c)
where d = 100
— could be mapped to
Tmp1(a,b,c,d) = R Join[b=c] S
Tmp2(a,b,c,d) = Sel[d=100](Tmp1)
Tmp3(a) = Proj[a](Tmp2)
Res(x) = Rename[Res(x)](Tmp3)
In general:
• SELECT clause becomes projection
• WHERE condition becomes selection or join
• FROM clause becomes join
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❖ Mapping Example
Consider the database schema:
Person(pid, name, address, …)
Subject(sid, code, title, uoc, …)
Terms(tid, code, start, end, …)
Courses(cid, sid, tid, …)
Enrolments(cid, pid, mark, ..)
and the query: Courses with more than 100 students in them?
which can be expressed in SQL as
select s.sid, s.code
from Course c join Subject s on (c.sid=s.sid)
join Enrolment e on (c.cid=e.cid)
group by s.sid, s.code
having count(*) > 100;
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❖ Mapping Example (cont)
The SQL might be compiled to
Tmp1(cid,sid,pid) = Course Join[c.cid = e.cid] Enrolment
Tmp2(cid,code,pid) = Tmp1 Join[t1.sid = s.sid] Subject
Tmp3(cid,code,nstu) = GroupCount[cid,code](Tmp2)
Res(cid,code) = Sel[nstu > 100](Tmp3)
or, equivalently
Tmp1(cid,code) = Course Join[c.sid = s.sid] Subject
Tmp2(cid,code,pid) = Tmp1 Join[t1.cid = e.cid] Enrolment
Tmp3(cid,code,nstu) = GroupCount[cid,code](Tmp2)
Res(cid,code) = Sel[nstu > 100](Tmp3)
Which is better?
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❖ Query Cost Estimation
The cost of evaluating a query is determined by
• the operations specified in the query execution plan
• size of relations (database relations and temporary relations)
• access mechanisms (indexing, hashing, sorting, join algorithms)
• size/number of main memory buffers (and replacement strategy)
Analysis of costs involves estimating:
• the size of intermediate results
• then, based on this, cost of secondary storage accesses
Accessing data from disk is the dominant cost in query evaluation
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❖ Query Cost Estimation (cont)
Consider execution plans for: σc (R ⨝d S ⨝e T) where R(c,d), S(d,e), T(e)
Tmp1(c,d,e) := hash_join[d](R,S)
Tmp2(c,d,e) := sort_merge_join[e](tmp1,T)
Res(c,d,e) := binary_search[c](Tmp2)
or
Tmp1(d,e) := sort_merge_join[e](S,T)
Tmp2(c,d,e) := hash_join[d](R,Tmp1)
Res(c,d,e) := linear_search[c](Tmp2)
or
Tmp1(c,d) := btree_search[c](R)
Tmp2(c,d,e) := hash_join[d](Tmp1,S)
Res(c,d,e) := sort_merge_join[e](Tmp2,T)
All produce same result, but have different costs.
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❖ Implementations of RA Ops
Sorting (quicksort, etc. are not applicable)
• external merge sort (cost O(NlogBN) with B memory buffers)
Selection (different techniques developed for different query types)
• sequential scan (worst case, cost O(N))
• index-based (e.g. B-trees, cost O(logN), tree nodes are pages)
• hash-based (O(1) best case, only works for equality tests)
Join (fast joins are critical to success of relational DBMSs)
• nested-loop join (cost O(N.M), buffering can reduce to O(N+M))
• sort-merge join (cost O(NlogN+MlogM))
• hash-join (best case cost O(N+M.N/B), with B memory buffers)
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❖ DBMS Architecture
Most RDBMSs are client-server systems:

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❖ DBMS Architecture (cont)
Layers within the DBMS server:

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Produced: 15 Feb 2021