Kyoung-Hwan Yun (#110)
 Conflicts
 Precedence Graphs and a Test for Conflict-
Serializability
 Conflict: a pair of consecutive actions
in a schedule such that, if their order is
interchanged, the final state produced
by the schedule is changed
 Non-conflicting situations:
 ri(X); rj(Y) will never conflict, even if
X = Y.
 ri(X); wi(Y) will not conflict for X ≠ Y.
 wi(X); rj(Y) will not conflict for X ≠ Y.
 wi(X); wj(Y) will not conflict for X ≠ Y.
 Three situations where actions may not
be swapped:
 Two actions of the same transactions
always conflict
ri(X); wi(Y)
 Three situations where actions may not
be swapped:
 Two writes of the same database
element by different transactions
conflict
wi(X); wj(X)
 Three situations where actions may not
be swapped:
 A read and a write of the same database
element by different transaction
conflict
ri(X); wj(X)
wi(X); rj(X)
 Two actions of different transactions
may be swapped unless:
 They involve the same database
element, AND
 At least one is a write.
 The schedules S and S’ are conflict-
equivalent, if S can be transformed into
S’ by a sequence of non-conflicting
swaps of adjacent actions.
 A schedule is conflict-serializable if it
is conflict-equivalent to a serial
schedule.
 Example of conflict-serializable schedule; schedule is
converted to the serial schedule (T1,T2) through a sequence
of swaps.
r1(A); w1(A); r2(A); w2(A); r1(B); w1(B); r2(B); w2(B);
r1(A); w1(A); r2(A); w2(A); r1(B); w1(B); r2(B); w2(B);
r1(A); w1(A); r2(A); r1(B); w2(A); w1(B); r2(B); w2(B);
r1(A); w1(A); r1(B); r2(A); w2(A); w1(B); r2(B); w2(B);
r1(A); w1(A); r1(B); r2(A); w1(B); w2(A); r2(B); w2(B);
r1(A); w1(A); r1(B); w1(B); r2(A); w2(A); r2(B); w2(B);
 Given a schedule S, involving transactions T1 and T2,
T1 takes precedence over T2 (T1 <S T2), if there are
actions A1 of T1 and A2 of T2, such that:
 A1 is ahead of A2 in S,
 Both A1 and A2 involve the same database element, and
 At least one of A1 and A2 is a write action.
 These are exactly the conditions under which we
cannot swap the order of A1 and A2. Therefore, a
conflict-equivalent serial schedule must have T1 before
T2.
 Precedence graph:
 Nodes represent transactions of S
 Arc from node i to node j if Ti <S Tj
Example Schedule
Precedence Graph
S: r2(A); r1(B); w2(A); r3(A); w1(B); w3(A); r2(B); w2(B);
T1
Acyclic  Conflict-serializable
T2
T3
Example Schedule
Precedence Graph
S: r2(A); r1(B); w2(A); r2(B); r3(A); w1(B); w3(A); w2(B);
T1
Cyclic  Not conflict-serializable
T2
T3
A schedule is conflict-serializable if and
only if its precedence graph is acyclic.