1. Atomic Snapshots

2. Abstract Data Types Abstract representation of data & set of methods (operations) for accessing it Implement using primitives on base objects 236825Introduction2 data

3. Correctness: Linearizability [Herlihy & Wing, 1990] For every concurrent execution there is a sequential execution that – Contains the same operations – Is legal (obeys the specification of the ADTs) – Preserves the real-time order of non-overlapping operations Each operation appears to takes effect instantaneously at some point between its invocation and its response (atomicity) 236825Introduction3

4. Atomic Snapshot n components Update a single component Scan all the components “at once” (atomically) Provides an instantaneous view of the whole memory 236825Introduction4 update ok scan v 1,…,v n

5. 236825Introduction5 Atomic Snapshot Algorithm Update(v,k) A[k] =  v,seq i, i  Scan() repeat read A[1],…,A[n] if equal return A[1,…,n] Linearize: Updates with their writes Scans inside the double collects double collect [Afek, Attiya, Dolev, Gafni, Merritt, Shavit, JACM 1993]

6. Atomic Snapshot: Linearizability Double collect (read a set of values twice) If equal, there is no write between the collects – Assuming each write has a new value (seq#) Creates a “safe zone”, where the scan can be linearized 236825Introduction6 read A[1],…,A[n] write A[j]

7. Liveness Conditions Wait-free: every operation completes within a finite number of (its own) steps  no starvation for mutex Nonblocking: some operation completes within a finite number of (some other process) steps  deadlock-freedom for mutex Obstruction-free: an operation (eventually) running solo completes within a finite number of (its own) steps – Also called solo termination wait-free  nonblocking  obstruction-free 236825Introduction7

8. Wait-free Atomic Snapshot [Afek, Attiya, Dolev, Gafni, Merritt, Shavit, JACM 1993] Embed a scan within the Update. 236825Introduction8 Update(v,k) V = scan A[k] =  v,seq i, i,V  Scan() repeat read A[1],…,A[n] if equal return A[1,…,n] else record diff if twice p j return V j Linearize: Updates with their writes Direct scans as before Borrowed scans in place Linearize: Updates with their writes Direct scans as before Borrowed scans in place direct scan borrowed scan

9. Atomic Snapshot: Borrowed Scans Interference by process p j And another one…  p j does a scan inbeteween Linearizing with the borrowed scan is OK. 236825Introduction9 write A[j] read A[j] …… …… embedded scan write A[j] read A[j] …… ……

10. © Hagit Attiya236755 (2013) 04: R/W simulations10 Complexity of Atomic Snapshots Scan needs O(n 2 ) reads and writes, why? Update needs O(n 2 ) reads and writes

11. O(nlogn) Atomic snapshots n components Scate - Update a single component and Scan all the components “at once” (atomically) Provides an instantaneous view of the whole memory 11 scate v 1,…,v n [Attiya, Rachman SIAM 1998]

12. One-shot Atomic Snapshot 12 scate v 1,…,v n

13. One-shot Atomic Snapshot 13 scate v 1,…,v n

14. The Classifier Procedure 14 K=2 1,1,1 lefties righties Local knowledge Original knowledge dominating knowledge Lemma: The output view of a righty dominates the union of the lefties outputs.

15. Atomic Snapshot from Classifiers 15 1 3 Scate operation requires O(nlogn) operations on single-writer multireader registers.

16. Atomic Snapshot from Classifiers Scate(val) S i =(val) For j=1 to n current i,1 [j]=S j v=root For l=1 to log(n) current i,l+1 =Classifier(label(v),current i,l ) if righty then v = v.right if lefty then v = v.left Return current i,log(n)+1 16 Operations are ordered in the leaves : Operations arriving at different leaves are comparable. Operations arriving at the same leaf have exactly the same final knowledge.

17. Linearization 17 1 3 scan update The views returned by the scate operations are comparable and ordered at the leaves from left to right