Position Graph: A New Mechanism for Concurrency Control

1
Position Graph A New Mechanism for Concurrency
Control

• S.N. Maheshwari
• Work done in collaboration with
• R.P. Rustagi

2
Position Graph

• Graph in which nodes represent transactions
• Nodes located on a line starting from 0 and
  extending indefinitely
• pos(Ti) is the position on the line at which the
  transaction Ti is located
• pos(Ti) lt pos(Tj) indicates that Tj follows Ti in
  the serial order of execution

3
T1
T2
T3
T4
T5
T6
A read step ri(x) of transaction Ti results in
insertion of edge Tj gt Ti if Tj TWL(x)
A write step wi(x) of transaction Ti results in
insertion of edge Tj gt Ti and Tk gt Ti if Tj ?
RL(x) and Tk TWL(x)
4
Two position graphs PGi (Vi, Ei) and PGj (Vj,
Ej) are said to be equivalent if

• There exists a one to one onto mapping f Vi -gt
  Vj and
• For any two nodes u, v ? Vi , such that pos(Tu )
  lt pos(Tv ) and there exists a path from u to v,
  then pos(Tf(u) ) lt pos(Tf(v) ) and there exists
  a path from f(u) to f(v)

5
Scheduling of transaction steps using position
graphs is done by attempting to maintain all
edges as forward edgesA back edge Tj -gt Ti has
to be converted into a forward edge

• This is possible as as long as there is no path
  from Ti to Tj. This involves
• Forward Movement
• Backward Movement

6
Scheduling Read and Write Steps

• Read Step
• Involves insertion of only one edge in the
  position graph as a read step conflicts only with
  the last write step
• Write step
• A write step conflicts with the last write step
  as well as all subsequent read steps after the
  last write step. Involves insertion of r 1 edges

7
It can be shown that amortised cost of scheduling

• Read Step
• 2 edge insertion
• Write Step
• 1 edge insertion

8
Timestamp Ordering

• Position graph based scheduler permits no node
  movement at all
• Need to maintain only max(RL(x)) representing the
  transaction with the highest time stamp which has
  read the entity x
• Position value of transaction WL(x) corresponds
  to the write timestamp

9
Two Phase Locking

• An edge Tj ? Ti corresponding to conflict on
  entity x represents that
• Tj has released a lock on x, and
• Ti has acquired a lock on x
• Since a transaction can not acquire a lock after
  it has released a lock we have
• An new edge can be incident at a node provided
  no edge has emanated from it

10
Descendent Free Node Movement (DFNM)
ProtocolRESTRICT NODE MOVEMENT IN A POSITION
GRAPH TO FORWARD MOVEMENT OF DESCENDENT FREE
NODES

• DFNM protocol
• Accepts all 2PL and Timestamp Schedules
• Is deadlock free
• Is Order Preserving

11
Implementation Issues

• Only need to maintain a boolean variable to keep
  track of whether descendents exist. No adjacency
  lists
• To prune the position graph and the associated
  structures transactions are characterised as live
  and active
• Active if a transaction has not completed
• Live if active or there is an ative transaction
  with smaller position value

12
Implementation continued

• Maintain a live transactions table and live data
  entity table
• With each transaction in the live transaction
  table maintain a list of data items written and
  read by it
• For each live data entity x maintain WL(x) and
  readlist(x)
• x is removed from the table if it is not being
  accessed by a live transaction

13
Implementation compared with 2PL

• In 2PL one has to maintain
• An active transaction table
• locks and wait-queues with each data item in lock
  table
• Maintaining the live transaction table is
  equivalent to maintaining active transaction able
  and issue of lock and unlock actions in 2PL
• WL(x) corresponds to exclusive lock on x, and
  readlists corresponds to shared locks

14
CSR
Extended DFNM-k
DFNM
TS
OPCSR
2PL