Efficient Implementation of Atomic Snapshots with Randomized Assistance
Explore the innovative approach of implementing atomic snapshots in O(log n) steps using randomized assistance, as discussed by James Aspnes, Yale Keren Censor-Hillel, and Technion researchers. The method involves snapshot objects, multi-writer registers, and tree structures to achieve efficient operations with controlled complexities and crash failure handling. The content delves into challenges, results, and techniques to enhance performance in concurrent systems.
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Atomic snapshots in O(log n) steps using randomized helping James Aspnes, Yale Keren Censor-Hillel, Technion 1
Snapshot Objects scan read all locations update(v) update your location p1 p2 pn 2
Model System of n processes, multi-writer registers Asynchronous schedule controlled by an adversary Crash failures require wait-free implementations Linearizable implementations R1 R2 R read write(v) v ok p1 p2 pn 3
Snapshots - Step Complexity Using multi-writer registers: can be done in O(n) steps [Inoue and Chen, WDAG 1994] and requires (n) steps [Jayanti, Tan, and Toueg, SICOMP 1996] Goal: a faster snapshot implementation (polylog) Limited-use: O(log3(n)) steps per operation, for polynomially many update operations [Aspnes, Attiya, Censor-Hillel, and Ellen, PODC 2012] This Talk: O(log3(n)) steps per operation, with high probability (without a usage bound) 4
Tree structure, Updates help Scans [Aspnes, Attiya, Censor-Hillel, and Ellen, PODC 2012] O(log n) steps? Array of views Pointer to array location 5X 0 1 2 3 4 5 s1+...+s4 0 1 2 3 0 1 2 s1+s2 s3+s4 s1 s2 s3 s4 5
Two Challenges 1. Coping with slow operations. Max-register: returns largest value previously written [Aspnes, Attiya, and Censor-Hillel, JACM 2012] Consecutive values differ by at most n 5 s1+...+s4 s1+s2 s3+s4 s1 s2 s3 s4 6
Two Challenges 2. Guaranteeing consistent views. Max-array: returns comparable pairs of max-register values [Aspnes, Attiya, Censor-Hillel, and Ellen, PODC 2012] 5 s1+...+s4 s1+s2 s3+s4 s1 s2 s3 s4 7
Our Results Randomized max-register in O(logn) steps with high probability Randomized 2-component max-array O(log2n) steps whp Randomized snapshot in O(log3n) steps whp Main technique: randomized helping 8
Max-Register read switch = 0 switch = 1 switch = 0 switch = 0 value 0 value 1 value v value v write(v) 9
Max-Register read switch = 0 switch = 1 switch = 0 switch = 1 switch = 0 value 0 value 1 value v value v write(v) write(v ) write(v ) 10
Randomized Max-Register switch = 0 switch = 1 switch = 0 switch = 1 m-valued max register switch = 0 write(v) 11
Randomized Max-Register switch = 0 switch = 1 k-bounded increments: value of write k + value of largest write switch = 0 switch = 1 m-valued max register switch = 0 O(log m + kn/m) = O(log n) steps per write write(v) 12
Writing to the Max-Register pj(cyclic) 1 TS: 1 read read v = max(returned value, v) 0 write(v) pi HELP: write(v) v', ts[j] TS[j] (random) size n3 POINTER: i 13
Reading the Max-Register pj read 1 TS: 1 +1 read 0 (logarithmic no. of steps) pi HELP: read (returns v, ts[j]) Main argument: many read steps many fresh values in pointer array, whp (random) size n3 POINTER: read (returns i) if ts[j]==TS[j] return v 14
2-Component Max Array write1(v) update second max-register write0(v) update first max-register read read both max-registers 15
Max Array Implementation read write1(v) Max1 Max1 switch = 0 switch = 0 Max1 Max1 switch = 0 Max1 value 0 Max1 value 1 Max1 value v value v Max1 Max1 Max1 write0(v) 16
Randomized 2-Component Max Array Problem: readers do not travel all the way from root to value switch = 0 switch = 1 Max1 Max1 Max1 switch = 0 switch = 1 Max1 Max1 Max1 Max1 Max1 Max1 switch = 0 Max1 Max1 Solution: read Max at root instead of Max at previous location Max1 write(v) 17
Summary Randomized snapshot in O(log3n) steps whp Main Technique: Randomized helping Open problems: Snapshot implementations using single-writer registers Additional randomized implementations Randomized lower bounds Thank you! Questions? 18
