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) < 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 –> Ti if Tj = TWL(x) A write step wi(x) of transaction Tiresults in insertion of edge Tj –> Ti and Tk –> 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 -> Vj and • For any two nodes u, v Vi , such that pos(Tu ) < pos(Tv ) and there exists a path from u to v, then pos(Tf(u) ) < 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 -> 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