Conflicting operations
------------------------

Two operations conflict with each other, if they are by two different
transactions and one of them is a write operation

r1(x) w2(x)

w1(x) r2(x)

w1(x) w2(x)


Serializability:
-----------------------------

A schedule S is serializable (equal to a serial schedule) iff all
conflicting operations in S occur in the same order as a serial
schedule.


Checking Serializability:
----------------------------

Create a conflict graph for a schedule S:

  -- Each transaction is a node
  
  -- For each conflict in S of the form:

     ri(x) wj(x)
     wi(x) rj(x)
     wi(x) wj(x)

     Draw an edge from Ti to Tj.


T1->T2, T2->T1



If the resulting graph has a cycle, then this schedule is NOT serializable.


If the resulting graph has no cycles, then this schedule is
serializable. I can order transaction using topological sort on the
conflict graph.



Examples:

S1: r1(x) r1(y) w2(y) w2(z) r3(z) w3(k) r1(k) w2(l) w1(x)

S1': r1(x) r1(y) w2(y) w2(z) r3(z) r1(k) w3(k) w2(l) w1(x)