1 / 19

The Concurrency Hierarchy and Algorithms for Unbounded Concurrency

The Concurrency Hierarchy and Algorithms for Unbounded Concurrency. Eli Gafni Michael Merritt Gadi Taubenfeld. Motivation & Overview. Exploring the consequences of the a priori bound assumption on processes and concurrency

michaelmccoy
Download Presentation

The Concurrency Hierarchy and Algorithms for Unbounded Concurrency

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Concurrency Hierarchy and Algorithms for Unbounded Concurrency Eli Gafni Michael Merritt Gadi Taubenfeld

  2. Motivation & Overview • Exploring the consequences of the a priori bound assumption on processes and concurrency • Extends “Computing with infinitely many processes” [MT2000] • Wait-free algorithms using atomic registers • Part 1: Computability: the Concurrency Hierarchy • Part 2: Algorithms: • Understanding one-shot/long-lived relationships • Infinity+Symmetry a Adaptivity • General algorithmic techniques for unbounded concurrency

  3. Concurrency:Simultaneously Active Processes • k-bounded – single boundkover all runs • bounded – in each run an upper bound exists • unbounded – finite at any point, no upper bound • infinite – within a single state (not considered)

  4. 2-concurrency bounded concurrency unbounded concurrency Part 1: The Concurrency Hierarchy 1-concurrency …

  5. Reminder: Snapshot algorithms sreturns {a,d,e,p,r,s,t,v,x,y} e returns {a,e,p,r,v,x} p y d r a xreturns {x} x e v t s Every process sees itself The snapshots are nested

  6. j t p w e u a z q x Adaptively rename to 2k-1 names Adaptively rename to 2k’-1 names 2k-1 2k’-1 k+k’=n 1 2 3… 2n-2 …then there is a 2n-2 renaming algorithm, contradicting [HS99] Lemma--Any snapshot algorithm has an all-inclusive run (n is known). Suppose not...

  7. 5 6 4 2 7 8 . . . 3 9 10 ... i new processes in thei’thset Corollary--Any snapshot algorithm for unbounded concurrency has the following run: 1

  8. 5 6 4 2 7 8 3 9 10 For bounded concurrency, the concurrency bound c limits the maximum difference between successive snapshots: . . . 1 ... because at mostcnew processes in each set

  9. 5 5 2 7 6 8 2 7 6 8 . . . 3 4 . . . 1 3 4 1 9 9 10 10 The Bounded Snapshot Problem: in complete runs, there is an upper bound on the difference between successive snapshots. Impossible in unbounded concurrency Solvable for bounded concurrency?

  10. k-concurrency bounded concurrency The Concurrency Hierarchy … k-snapshot (k+1)-concurrency … bounded snapshot unbounded concurrency

  11. long-lived snapshot adaptive long-lived renaming adaptive one-shot renaming [AF99, AF2000] adaptive long-lived collect adaptive one-shot snapshot [AST99] adaptive long-lived snapshot adaptive one-shot 2k-1 renaming [AST99] Part 2: Algorithms for Unbounded Concurrency unbounded concurrency one-shot snapshot

  12. . Use diagonalization to make long-lived . . . . . . . Take a second snapshot (which must include me): ...if the road goes on forever, someone paved it after driving past my house One-shotSnapshot for Unbounded Concurrency . . .

  13. 0 2 5 9 1 4 8 3 7 . . . 6 Infinite array of splitters: May not terminate Adaptive One-shot Renaming [MA95, AF98]

  14. p7 1 5 11 19 3 9 17 7 15 . . . 14 13 As soon aspifails to acquire any name j > 2ipitakesname 2i Adaptive One-shot Renaming for Unbounded Concurrency via “Interleaving” Infinite array of odd-numbered splitters:

  15. Adaptive One-shot Snapshot for Unbounded Concurrency . . . . 1 5 11 19 3 9 17 . . . 7 15 13 Adaptive renaming . . . One-shot snapshot

  16. for Unbounded Concurrency One-shot snapshot . 1 5 11 19 . . . 3 9 17 7 15 . . . . . . 13 Adaptive, Optimal One-shot Renaming collect 2k-1 one-shot renaming [BD89]

  17. 1-concurrency 1-snapshot 2-snapshot … bounded snapshot a. collect a. snapshot a. renaming a. 1-shot 2k-1 renaming Summary 2-concurrency … bounded concurrency unbounded concurrency

  18. Conclusions and Open Problems • Concurrency hierarchy • Algorithms for unbounded concurrency (work for unknown number/concurrency) • General techniques • one-shot + infinite-arrival a long-lived (diagonalization) • interleaving, help first, doorways • Are there natural problems outside unbounded concurrency? • Efficiency (space and time) • Separating problems that are “tasks”

  19. One-shot Renaming “black-box” Transformation 1 A1 g(k) names 0 A2 k processes 1 A3 g(k) names … 1 Ap g(k) names … At most k algorithms entered Eran Yahav

More Related