Degrees of Isolation – A Theoretical Formulation

Presented by

Balaji Sethuraman

Paper Information

A Theoretical Formulation of Degrees of Isolation in Databases

byVijayalakshmi Aturi, Elisa Bertino and Sushil JagodiaLink: http://citeseer.nj.nec.com/cachedpage/49154/1

Abstract:Formulation of various degrees of isolation in terms of Histories Lock based protocols Timestamp based protocols

Transaction Model

A transaction is a unit of program execution that accesses and possibly updates various data items.

Transaction properties Atomicity: All or none operations. Consistency: Preserves consistency of database. Isolation: Concurrency of transactions. Each

transaction is unaware of the existence of the other transactions.

Durability: Changes are persisted even if there are system failures.

Focus on the Isolation property of transaction.

Isolation True isolation (serialized execution) of transactions slows

down performance of the system. In a shared database system, a completely Isolated

system gives the illusion to each transaction that it is being executed alone all by itself.

Most commercial databases offer different degrees of isolation.

Degrees (levels) of isolation offers compromise between Correctness and Performance of a transaction.

4 levels of Isolation are defined. Lower level of isolation implies improved response time achieved at the expense of consistency.

Degrees of Isolation Degree 0 – Chaos

Does not allow a more than one transaction to simultaneously to write on a data item.

Least restrictive of all isolations Degree 1 – Browse

Does not allow data updated by a uncommitted transaction to be overwritten (no lost updates).

Equivalent to READ_UNCOMMITTED isolation level of ANSI/ISO SQL2 standard.

Degrees of Isolation

Degree 2 – Cursor Stability In addition to Degree 1, restricts transactions to

read only committed data. Equivalent to READ_COMMITTED isolation level

of ANSI/ISO SQL2 standard Degree 3 – Repeatable Reads

Provides complete isolation (Serializable). Most restrictive of all. Equivalent to REPEATABLE_READ isolation level

of ANSI/ISO SQL2 standard.

Notations Ti – Transaction i.

ri[x] – read operation by Ti on data item x.

wi[x] – write operation by Ti on data item x.

oi[x] – any operation by Ti on data item x.

ci – commit operation by Ti.

<H – happens-before relation.

ri[x] <H wj[x] – Ti read on x happens before Tj write on x.

Definitions Two operations oi[x] and oj[x] conflict with each other

if i <> j and atleast one of them is write.

A history H over T = {T0,T1…Tn} is a partial order with ordering relation <H where H = Un

i=0 Ti and <H subset-of Un

i=0 <i

e.g: T1 = r1[z] < w1[x] < w1[y] < r1[z] < c1

T2 = w2[a] < w2[z] < r2[y] < w2[x] < c2

H1 = r1[z] <H w1[x] <H w1[y] <H w2[a] <H w2[z] <H r2[y] <H r1[z] <H c1 <H w2[x] <H c2

or H1 = r1[z] w1[x] w1[y] w2[a] w2[z] r2[y] r1[z] c1 w2[x] c2

Degree Definition & Isolation graphs

Each degree is defined in terms of the operations allowed in its history.

The Isolation graphs IG(H) defines how to construct a directed graph from the History H over T = {T0,T1…Tn}

Isolation level Theorem: A History H over T is a degree i (i=0 to 3 inclusive) isolation history if IGi(H) is acyclic. e.g.: A History is degree 2 isolation history if

IG2(H) is acyclic.

Degree 0 A history H is a degree 0 isolation history if whenever w i[x], wj[x] ε

H, either wi[x] <H wj[x] or wj[x] <H wi[x]. Isolation Graph of degree 0:

Let H be a history over T. Its degree 0 isolation graph IG0(H) is a directed graph whose nodes are transactions in T and whose edges are Ti -> Tj whenever H contains a pair of operations wi[x] and wj[x], i<>j, such that (wi[x] !<<H wj[x]) ^ (wj[x] !<<H wi[x]).

e.g.: H1 = w1[x]

w2[x] c1 c2

IG0(H1) = T1 <-> T2

IG0(H) has a cycle. H1 is NOT degree 0 isolation history.

e.g.: H1 = r1[z] w1[x] w1[y] w2[a] w2[z] r2[y] r1[z] c1 w2[x] c2

IG0(H1) = T1 T2

IG0(H) is acyclic. H1 is a degree 0 isolation history.

Degree 1 A history H is a degree 1 isolation history if

whenever wi[x], wj[x] ε H, either wi[x] <H wj[x] or wj[x] <H

wi[x] and whenever wi[x] <H wj[x], ci <H wj[x].

Isolation Graph of degree 1:Let H be a history over T. Its degree 1 isolation graph

IG1(H) is a directed graph whose nodes are transactions in T and whose edges are as follows

Every edge in IG0(H) is an edge in IG1(H). There is an edge Ti -> Tj whenever there exist

operations wi[x] and wj[x], i<>j, such that wi[x] <H wj[x] or cj !<H wi[x].

e.g: H = w1[x] w2[x] c1 w3[x] c3

IG1(H) = Cycle exists. H is not in Isolation Degree 1

T1

T2

T3

e.g: T1 = r1[z] w1[x] w1[y] r1[z] c1

T2 = w2[a] w2[z] r2[y] w2[x] c2

H1 = r1[z] w1[x] w1[y] w2[a] w2[z] r2[y] w2[x] r1[z] c1 c2

IG1(H1) = T1 <-> T2

IG1(H1) has a cycle. H1 is NOT degree 1 isolation history.

H2 = r1[z] w1[x] w1[y] w2[a] w2[z] r2[y] r1[z] c1 w2[x] c2

IG1(H2) = T1 -> T2

IG1(H2) is acyclic. H2 is a degree 1 isolation history.

Degree 2 A history H is a degree 2 isolation history if

whenever two conflicting operations oi[x], oj[x] ε H, either oi[x] <H oj[x] or oj[x] <H oi[x] and

whenever wi[x] <H oj[x], ci <H oj[x]. Isolation Graph of degree 2:

Let H be a history over T. Its degree 2 isolation graph IG2(H) is a directed graph whose nodes are transactions in T and whose edges are as follows Every edge in IG1(H) is an edge in IG2(H). There is an edge Ti -> Tj whenever H contains two conflicting operations

there exist operations oi[x] and oj[x], i<>j, such that (oi[x] !<<H oj[x]) ^ (oj[x] !<<H oi[x]).

There is an edge Ti -> Tj, i<>j whenever either (wi[x] <H rj[x]) or (cj[x] !<<H

oi[x] and wj[x] ε Tj).e.g.: H3 = r1[z] w1[x] w1[y] w2[a] w2[z] r2[y] r1[z] c1 w2[x] c2

IG3(H3) has a cycle. H3 is NOT degree 3 isolation history. H4 = r1[z] w1[x] w1[y] w2[a] w2[z] r1[z] c1 r2[y] w2[x] c2

IG3(H4) is acyclic. H4 is a degree 3 isolation history.

Degree 3 A history H is a degree 3 isolation history if

H is serializable and whenever wi[x] <H oj[x], ci <H oj[x].

Isolation Graph of degree 3:Let H be a history over T. Its degree 3 isolation graph IG3(H) is a directed graph whose nodes are transactions in T and whose edges are as follows Every edge in IG2(H) is an edge in IG3(H). There is an edge Ti -> Tj,, i<>j whenever either (ri[x] <H wj[x]) or

(cj[x] !<<H oi[x] and wj[x] ε Tj).

e.g.: H4 = r1[z] w1[x] w1[y] w2[a] w2[z] r1[z] c1 r2[y] w2[x] c2

IG3(H4) has a cycle. H4 is NOT degree 3 isolation history.

H5 = r1[z] w1[x] w1[y] w2[a] r1[z] w2[z] c1 r2[y] w2[x] c2

IG3(H5) is acyclic. H5 is a degree 3 isolation history.

Transaction Isolation Levels In a History, different transactions can have different

isolation levels. A transaction Ti is history H is given

Degree 0 isolation if whenever there exists two write operations wi[x] and wj[x] in H, either wi[x] <H

wj[x] or wj[x] <H wi[x]. Degree 1 isolation if

Whenever there exists two operations wi[x] and wj[x] in H such that wj[x] <H wi[x], cj <H wi[x] and

Whenever there exists two operations wi[x] and wj[x] in H such that wi[x] <H wj[x], ci <H wj[x].

Transaction Isolation Levels degree 2 isolation if

Ti is given degree 1 isolation and Whenever there exist two operations wj[x] and

ri[x] in H such that whenever wj[x] <H ri[x], cj <H ri[x].

degree 3 isolation if Ti is given degree 2 isolation and Whenever oi[x] and oj[x] are conflicting

operations such that oi[x] <H oj[x], then !Э oi[y] such that oj[y] <H oi[y] where oi[y], oj[y] are two conflicting operations in H.

Transaction Isolation Levels

Example :

T1 = r1[y] w1[z] w1[y] c1

T2 = r2[x] w2[x] c2

T3 = w3[x] w3[y] c3

H9 = r2[x] w3[x] w3[y] r1[y] c3 w2[x] c2 w1[z] w1[y] c1

T1 is in Degree 1 isolation (not Degree 2)

T2 is in Degree 2 isolation (not Degree 3)

T3 is in Degree 3 isolation

Protocols Two protocols to achieve different degrees of

isolation Lock-based protocols. Timestamp based protocols.

Most database systems use lock based protocol to implement concurrency control for transactions.

Lock based Protocols Two types of locks – a shared lock (read) and an

exclusive-lock (write). Notations:

sli[x] = shared lock acquisition of x by Ti

xli[x] = exclusive lock acquisition of x by T i

uli[x] = release of shared or exclusive lock on x by T i

Two locks li[x] and lj[x] are compatible if i=j or neither of them is an exclusive lock.

A transaction is well-formed if it acquires a shared-lock before reading data item and acquires a exclusive-lock before writing a data item.

Paper defines theorems for achieving various degrees of isolation using lock based protocols and proves them.

Timestamp based Protocols Every data item is associated with read, write, commit

timestamps use boolean values to order the operations from scheduler

to DM. Notations :

rts[x] = Read timestamp of x wts[x] = Write timestamp of x ts[Ti] = Unique timestamp for Transaction Ti cts[Ti] = Commit timestamp of Transaction Ti r-in-transit[x] = Read operation in transit from Scheduler

to DM on data item x. w-in-transit[x] = Write operation in transit from Scheduler

to DM on data item x. Paper defines theorems for achieving various degrees of

isolation using timestamp based protocols and proves them.

Conclusion

Contributions of the paper Formalization of notions of various degrees of

isolation in terms of histories. Timestamp-based protocols for achieving different

degree of isolation.