Degrees of Isolation – A Theoretical Formulation Presented by Balaji Sethuraman

Paper Information A Theoretical Formulation of Degrees of Isolation in Databases by Vijayalakshmi Aturi, Elisa Bertino and Sushil Jagodia Link: 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 T i – Transaction i. r i [x] – read operation by T i on data item x. w i [x] – write operation by T i on data item x. o i [x] – any operation by T i on data item x. c i – commit operation by T i. < H – happens-before relation. r i [x] < H w j [x] – T i read on x happens before T j write on x.

Definitions Two operations o i [x] and o j [x] conflict with each other if i <> j and atleast one of them is write. A history H over T = {T 0,T 1 …T n } is a partial order with ordering relation < H where H = U n i=0 T i and < H subset-of U n i=0 < i e.g: T 1 = r 1 [z] < w 1 [x] < w 1 [y] < r 1 [z] < c 1 T 2 = w 2 [a] < w 2 [z] < r 2 [y] < w 2 [x] < c 2 H 1 = r 1 [z] < H w 1 [x] < H w 1 [y] < H w 2 [a] < H w 2 [z] < H r 2 [y] < H r 1 [z] < H c 1 < H w 2 [x] < H c 2 or H 1 = r 1 [z] w 1 [x] w 1 [y] w 2 [a] w 2 [z] r 2 [y] r 1 [z] c 1 w 2 [x] c 2

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 = {T 0,T 1 …T n } 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], w j [x] ε H, either w i [x] < H w j [x] or w j [x] < H w i [x]. Isolation Graph of degree 0: T j whenever H contains a pair of operations w i [x] and w j [x], i<>j, such that (w i [x] !< H w j [x]) ^ (w j [x] !< H w i [x]). e.g.: H 1 = w 1 [x] w 2 [x] c 1 c 2 IG0(H 1 ) = T1 T2 IG0(H) has a cycle. H 1 is NOT degree 0 isolation history. e.g.: H 1 = r 1 [z] w 1 [x] w 1 [y] w 2 [a] w 2 [z] r 2 [y] r 1 [z] c 1 w 2 [x] c 2 IG0(H 1 ) = T 1 T 2 IG0(H) is acyclic. H 1 is a degree 0 isolation history.

Degree 1 A history H is a degree 1 isolation history if whenever w i [x], w j [x] ε H, either w i [x] < H w j [x] or w j [x] < H w i [x] and whenever w i [x] < H w j [x], c i < H w j [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 T i -> T j whenever there exist operations w i [x] and w j [x], i<>j, such that w i [x] < H w j [x] or c j !< H w i [x]. e.g: H = w 1 [x] w 2 [x] c 1 w 3 [x] c 3 IG1(H) = Cycle exists. H is not in Isolation Degree 1 T1T1 T2T2 T3T3

e.g: T 1 = r 1 [z] w 1 [x] w 1 [y] r 1 [z] c 1 T 2 = w 2 [a] w 2 [z] r 2 [y] w 2 [x] c 2 H 1 = r 1 [z] w1[x] w 1 [y] w 2 [a] w 2 [z] r 2 [y] w 2 [x] r 1 [z] c 1 c 2 IG1(H 1 ) = T 1 T 2 IG1(H 1 ) has a cycle. H 1 is NOT degree 1 isolation history. H 2 = r 1 [z] w1[x] w 1 [y] w 2 [a] w 2 [z] r 2 [y] r 1 [z] c 1 w 2 [x] c 2 IG1(H 2 ) = T 1 -> T 2 IG1(H 2 ) is acyclic. H 2 is a degree 1 isolation history.

Degree 2 A history H is a degree 2 isolation history if whenever two conflicting operations o i [x], o j [x] ε H, either o i [x] < H o j [x] or o j [x] < H o i [x] and whenever w i [x] < H o j [x], c i < H o j [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). T j whenever H contains two conflicting operations there exist operations o i [x] and o j [x], i<>j, such that (o i [x] !< H o j [x]) ^ (o j [x] !< H o i [x]). T j, i<>j whenever either (w i [x] < H r j [x]) or (c j [x] !< H o i [x] and w j [x] ε Tj). e.g.: H 3 = r 1 [z] w 1 [x] w 1 [y] w 2 [a] w 2 [z] r 2 [y] r 1 [z] c 1 w 2 [x] c 2 IG3(H 3 ) has a cycle. H 3 is NOT degree 3 isolation history. H 4 = r 1 [z] w1[x] w 1 [y] w 2 [a] w 2 [z] r 1 [z] c 1 r 2 [y] w 2 [x] c 2 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 w i [x] < H o j [x], c i < H o j [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). T j,, i<>j whenever either (r i [x] < H w j [x]) or (c j [x] !< H o i [x] and w j [x] ε Tj). e.g.: H 4 = r 1 [z] w1[x] w 1 [y] w 2 [a] w 2 [z] r 1 [z] c 1 r 2 [y] w 2 [x] c 2 IG3(H 4 ) has a cycle. H 4 is NOT degree 3 isolation history. H 5 = r 1 [z] w1[x] w 1 [y] w 2 [a] r 1 [z] w 2 [z] c 1 r 2 [y] w 2 [x] c 2 IG3(H 5 ) is acyclic. H 5 is a degree 3 isolation history.

Transaction Isolation Levels In a History, different transactions can have different isolation levels. A transaction T i is history H is given Degree 0 isolation if whenever there exists two write operations w i [x] and w j [x] in H, either w i [x] < H w j [x] or w j [x] < H w i [x]. Degree 1 isolation if Whenever there exists two operations w i [x] and w j [x] in H such that w j [x] < H w i [x], c j < H w i [x] and Whenever there exists two operations w i [x] and w j [x] in H such that w i [x] < H w j [x], c i < H w j [x].

Transaction Isolation Levels degree 2 isolation if T i is given degree 1 isolation and Whenever there exist two operations w j [x] and r i [x] in H such that whenever w j [x] < H r i [x], c j < H r i [x]. degree 3 isolation if Ti is given degree 2 isolation and Whenever o i [x] and o j [x] are conflicting operations such that o i [x] < H o j [x], then !Э o i [y] such that o j [y] < H o i [y] where o i [y], o j [y] are two conflicting operations in H.

Transaction Isolation Levels Example : T1 = r 1 [y] w 1 [z] w 1 [y] c 1 T2 = r 2 [x] w 2 [x] c 2 T3 = w 3 [x] w 3 [y] c 3 H9 = r 2 [x] w 3 [x] w 3 [y] r 1 [y] c 3 w 2 [x] c 2 w 1 [z] w 1 [y] c 1 T 1 is in Degree 1 isolation (not Degree 2) T 2 is in Degree 2 isolation (not Degree 3) T 3 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: sl i [x] = shared lock acquisition of x by T i xl i [x] = exclusive lock acquisition of x by T i ul i [x] = release of shared or exclusive lock on x by T i Two locks l i [x] and l j [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[T i ] = Unique timestamp for Transaction T i cts[T i ] = Commit timestamp of Transaction T i 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.