- The
reason
why do we use
conflict-serializability:
- There is a simple procedure
the test/check whether
a schedule S is:
- conflict-serializable
- or not conflict-serializable
- There is a simple procedure
the test/check whether
a schedule S is:
- Observation:
- If we find
2 conflicting actions
(anywhere in a schedule):
then (because opj (X) can never be swap with opi (X)):
- Transaction Ti must precede transaction Tj in a serial schedule
- Therefore, the
ordering in a
serial schedule must be
as follows:
- If we find
2 conflicting actions
(anywhere in a schedule):
- The precedence relationship:
- This observation has determined a
- precedence relationship between transactions Ti and Tj
Specifically:
- Transaction Ti must precede transaction Tj (in a serial schedule)
- This observation has determined a
- Notation:
- We use a graph
to represent
all precedence relationships
found in a
schedule S:
- For every pair
of conflicting actions in
a schedule S:
we add the edge Ti → Tj to the graph
- For every pair
of conflicting actions in
a schedule S:
- Example:
- Schedule:
- Make it easier by
grouping the
action by their
different DB elements:
- Now you can see the
precedence relationships
easier
(find all
conflicting operations):
- Graph with
all precedence relationships:
- Schedule:
- Fact:
- A schedule S is
conflict-serializable
iff:
- The corresponding precedence graph of schedule S does not contain any cycles
- A schedule S is
conflict-serializable
iff:
- Example 1:
- Schedule:
- Precedence graph for the
schedule:
The serial schedule is: T1 T2 T3
- Proof:
swap
the non-conflicting operations:
- Schedule:
- Example 2:
- Schedule:
Group the actions by their DB elements:
- Precedence graph for the
schedule:
This schedule is not conflict-serializable because there is a cycle
- Proof:
- To make a serial schedule with the
order
T1 ... T2
we must
swap this
pair of
conflicting action:
- To make a serial schedule with the
order
T2 ... T1
we must
swap this
pair of
conflicting action:
Therefore: there is no way to swap non-conflicting actions to convert the schedule into a serial schedule !!!
- To make a serial schedule with the
order
T1 ... T2
we must
swap this
pair of
conflicting action:
- Schedule: