flp impossibility of consensus
play

FLP Impossibility of Consensus Yan Ji Oct 26, 2017 Slides - PowerPoint PPT Presentation

Dec 14, 2023 •215 likes •1.73k views

FLP Impossibility of Consensus Yan Ji Oct 26, 2017 Slides inspired by Lorenzo Alvisi (CS5414 FA16) slides and Philip Daian (CS6410 FA16) slides I think you ought to know I'm feeling very depressed. I think you ought to know I'm feeling

  1. Model It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. p 1 0/1, b/0/1 ... Step: C’= e(C) = (s’, M’) ● (p i , m) p i M 0/1, b/0/1 ... p 1 p 1 p k 0/1, b/0/1 C = (s, M) 0/1, b/0/1 C = (s, M) 0/1, b/0/1 . . s . . . . M M p k p k 0/1, b/0/1 0/1, b/0/1 s s

  2. Model It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. p 1 0/1, b/0/1 ... Step: C’= e(C) = (s’, M’) ● (p i , m) p i M 0/1, b/0/1 ... p 1 p 1 p k 0/1, b/0/1 C = (s, M) 0/1, b/0/1 C = (s, M) 0/1, b/0/1 . ... s . (p i , m) p i 0/1, b M . M ... (p i , m) p k p k 0/1, b/0/1 0/1, b/0/1 s s

  3. Model It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. p 1 0/1, b/0/1 ... Step: C’= e(C) = (s’, M’) ● (p i , m) p i M 0/1, b/0/1 ... p 1 p 1 p k 0/1, b/0/1 C = (s, M) 0/1, b/0/1 C = (s, M) 0/1, b/0/1 . ... s . p’ i 0/1, b 0 M . M ... (p i , m) p k p k 0/1, b/0/1 0/1, b/0/1 s s’

  4. Model It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. p 1 0/1, b/0/1 ... Step: C’= e(C) = (s’, M’) ● (p i , m) p i M 0/1, b/0/1 ... p 1 p 1 p k 0/1, b/0/1 C = (s, M) 0/1, b/0/1 C = (s, M) 0/1, b/0/1 . ... s . send p’ i 0/1, b 0 M . M ... (p i , m) p k p k 0/1, b/0/1 0/1, b/0/1 s s’

  5. Model It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. p 1 0/1, b/0/1 ... Step: C’= e(C) = (s’, M’) ● (p i , m) p i M 0/1, b/0/1 ... p 1 p 1 p k 0/1, b/0/1 C = (s, M) 0/1, b/0/1 C’ = (s’, M’) 0/1, b/0/1 . ... s . p’ i 0/1, b 0 M’ . M ... (p i , m) p k p k 0/1, b/0/1 0/1, b/0/1 s s’

  6. Model It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. p 1 0/1, b/0/1 ... Step: C’= e(C) = (s’, M’) ● (p i , m) p i M 0/1, b/0/1 ... p 1 p 1 p k 0/1, b/0/1 C = (s, M) 0/1, b/0/1 C’ = (s’, M’) 0/1, b/0/1 . ... s . p’ i 0/1, b 0 M’ . M ... (p i , m) p k p k 0/1, b/0/1 0/1, b/0/1 s s’

  7. Proof It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. How to prove impossibility?

  8. Proof It is impossible to have a deterministic protocol that solves consensus in a message-passing asynchronous system in which at most one process may fail by crashing. How to prove impossibility? Assume to the contrary that there exists a consensus protocol P such that… How to define P?

  9. More terms A schedule S of P is a finite or infinite sequence of events (e 1 , e 2 , …, e k )of P, ● S(C) = e k (...(e 2 (e 1 (C)))...)

  10. More terms A schedule S of P is a finite or infinite sequence of events (e 1 , e 2 , …, e k )of P, ● S(C) = e k (...(e 2 (e 1 (C)))...) A run of P is a sequence of steps associating a schedule S, in other words, a ● run is a pair of a configuration C and a schedule S, written as (C, S)

  11. More terms A configuration C’ is reachable from a configuration C if there exist a ● schedule S such that C’ = S(C)

  12. More terms A configuration C’ is reachable from a configuration C if there exist a ● schedule S such that C’ = S(C) A configuration C ′ is accessible from an initial configuration C 0 if C’ is ● reachable from C 0

  13. More terms A configuration C’ is reachable from a configuration C if there exist a ● schedule S such that C’ = S(C) A configuration C ′ is accessible from an initial configuration C 0 if C’ is ● reachable from C 0 e 1 (p 1 , m 1 ) e 2 (p k , m 2 ) p’ 1 p 1 p’ 1 0/1, b 0/1, b C 0 = (s 0 , M 0 ) C 2 = (s 2 , M 2 ) C 1 = (s 1 , M 1 ) 0/1, b . . . . . . . . M 2 . M 0 M 1 p’ k p k p k 0/1, b 0 0/1, b 0/1, b s 2 s 0 s 1

  14. More terms A configuration C has decision value v if some process p is in a decision ● state with output=v, which is “write-once”/irreversible

  15. More terms A configuration C has decision value v if some process p is in a decision ● state with output=v, which is “write-once”/irreversible A run is a deciding run if some process reaches a decision state. ●

  16. More terms A configuration C has decision value v if some process p is in a decision ● state with output=v, which is “write-once”/irreversible A run is a deciding run if some process reaches a decision state. ● e 1 (p 1 , m 1 ) p 1 p’ 1 0/1, b C 0 = (s 0 , M 0 ) C 1 = (s 1 , M 1 ) 0/1, b . . . . . . M 0 M 1 p k p k 0/1, b 0/1, b s 0 s 1

  17. More terms A configuration C has decision value v if some process p is in a decision ● state with output=v, which is “write-once”/irreversible A run is a deciding run if some process reaches a decision state. ● e 1 (p 1 , m 1 ) e 2 (p k , m 2 ) p’ 1 p 1 p’ 1 0/1, b 0/1, b C 0 = (s 0 , M 0 ) C 2 = (s 2 , M 2 ) C 1 = (s 1 , M 1 ) 0/1, b . . . . . . . . M 2 . M 0 M 1 p’ k p k p k 0/1, b 0 0/1, b 0/1, b s 2 s 0 s 1

  18. More terms A consensus protocol P is partially correct if: ● No accessible configuration has more than one decision value ○ (agreement) For each v in {0, 1}, some accessible configuration has decision ○ value v (validity) A run is admissible if every process, except possibly one (faulty ● process), takes infinitely many steps in S

  19. Assume to the contrary that there exists P such that P is partially correct ● Agreement + Validity ○

  20. Assume to the contrary that there exists P such that P is partially correct ● Agreement + Validity ○ Every admissible run of P is a deciding run ● Termination ○

  21. Assume to the contrary that there exists P such that P is partially correct ● Agreement + Validity ○ Every admissible run of P is a deciding run ● Termination ○ What kind of contradiction should possibly be like? ●

  22. Categories of configurations Univalent, or i-valent (i in {0, 1}) ● A configuration C is univalent or i-valent if some process has ○ decided i in C, or if all configurations accessible from C are i-valent

  23. Categories of configurations Univalent, or i-valent (i in {0, 1}) ● A configuration C is univalent or i-valent if some process has ○ decided i in C, or if all configurations accessible from C are i-valent ... S 1 p 1 0, b C = (s, M) . . S 2 ... Decide on 0 . M p k 0, b ... S 3 s

  24. Categories of configurations Univalent, or i-valent (i in {0, 1}) ● A configuration C is univalent or i-valent if some process has ○ decided i in C, or if all configurations accessible from C are i-valent ... S 1 p 1 1, b C = (s, M) . . S 2 ... Decide on 1 . M p k 1, b ... S 3 s

  25. Categories of configurations Bivalent ● A configuration C is bivalent if some of the configurations ○ accessible from it are 0-valent while others are 1-valent ... S 1 Decide on 0 p 1 0, b C = (s, M) . . S 2 ... Decide on 1 . M p k 1, b ... S 3 Decide on 0 s

  26. Categories of configurations Bivalent (see Bivalent, read Undeciding) ● A configuration C is bivalent if some of the configurations ○ accessible from it are 0-valent while others are 1-valent ... S 1 Decide on 0 p 1 0, b C = (s, M) . . S 2 ... Decide on 1 . M p k 1, b ... S 3 Decide on 0 s

  27. What kind of contradiction should possibly be like? INDISTINGUISHABILITY between processes: Crashed ● Simply slow in processing or having a terrible network condition ●

  28. What kind of contradiction should possibly be like? INDISTINGUISHABILITY between processes: Crashed ● Simply slow in processing or having a terrible network condition ● For any protocol, there exists a configuration that is always bivalent.

  29. What kind of contradiction should possibly be like? INDISTINGUISHABILITY between processes: Crashed ● Simply slow in processing or having a terrible network condition ● For any protocol, there exists a configuration that is always bivalent. Remaining UNDECIDED in the value

  30. What kind of contradiction should possibly be like? INDISTINGUISHABILITY between processes: Crashed ● Simply slow in processing or having a terrible network condition ● For any protocol, there exists a configuration that is always bivalent. Remaining UNDECIDED in the value

  31. Proof Outline For any protocol, there is an initial configuration that is bivalent ● Then there is another bivalent configuration reachable from it after ● applying some event And another reachable bivalent configuration ● … ● An infinite undeciding run ●

  32. Most exciting part!!! Lemma 1 (commutativity of schedules) ● Suppose that from some C, the schedules S 1 , S 2 lead to C 1 , C 2 ○ respectively. If the steps in S 1 and in S 2 are disjoint, then S 2 can be applied to C 1 and S 1 can be applied to C 2 and both lead to the same C 3 .

  33. Most exciting part!!! Lemma 1 (commutativity of schedules) ● Suppose that from some C, the schedules S 1 , S 2 lead to C 1 , C 2 ○ respectively. If the steps in S 1 and in S 2 are disjoint, then S 2 can be applied to C 1 and S 1 can be applied to C 2 and both lead to the same C 3 . C S 1 S 2 C 1 C 2 S 2 S 1 C 3

  34. Proof Outline For any protocol, there is an initial configuration that is bivalent ● Then there is another bivalent configuration reachable from it after ● applying some event And another reachable bivalent configuration ● … ● An infinite undeciding run ●

  35. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○

  36. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. p 1 0, b 0, b 0, b 0, b 1, b 1, b 1, b 1, b p 2 0, b 0, b 1, b 1, b 1, b 1, b 0, b 0, b 1, b 0, b 0, b 1, b 1, b 0, b 0, b 1, b p 3

  37. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. p 1 0, b 0, b 0, b 0, b 1, b 1, b 1, b 1, b p 2 0, b 0, b 1, b 1, b 1, b 1, b 0, b 0, b 1, b 0, b 0, b 1, b 1, b 0, b 0, b 1, b p 3 1 1 0 0 0 0 1 1

  38. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. p 1 0, b 0, b 0, b 0, b 1, b 1, b 1, b 1, b p 2 0, b 0, b 1, b 1, b 1, b 1, b 0, b 0, b 1, b 0, b 0, b 1, b 1, b 0, b 0, b 1, b p 3 1 1 0 0 0 0 1 1

  39. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. p 1 0, b 0, b 0, b 0, b 1, b 1, b 1, b 1, b p 2 0, b 0, b 1, b 1, b 1, b 1, b 0, b 0, b 1, b 0, b 0, b 1, b 1, b 0, b 0, b 1, b p 3 1 0 0 0 1 1 1 0

  40. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. p 1 0, b 0, b 0, b 0, b 1, b 1, b 1, b 1, b p 2 0, b 0, b 1, b 1, b 1, b 1, b 0, b 0, b 1, b 0, b 0, b 1, b 1, b 0, b 0, b 1, b p 3 1 0 0 0 1 1 1 0

  41. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. Adjacent: differ in the C 1 C 2 initial state of a single process

  42. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... differ in the C 1 C 2 C i C i+1 C k initial state of a single process

  43. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  44. Most exciting part!!! Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  45. Most exciting part!!! differ in the initial state C i C i+1 of a single process p Lemma 2 ● P has a bivalent initial configuration. ○ Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  46. Most exciting part!!! differ in the initial state C i C i+1 of a single process p S in Lemma 2 ● which p takes no P has a bivalent initial configuration. ○ step C/p Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  47. Most exciting part!!! differ in the initial state C i C i+1 of a single process p S in S in Lemma 2 ● which p which p takes no takes no P has a bivalent initial configuration. ○ step step C/p Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  48. Most exciting part!!! differ in the initial state C i C i+1 of a single process p S in S in Lemma 2 ● which p which p takes no takes no P has a bivalent initial configuration. ○ step step C/p Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... 0 differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  49. 0/1 Most exciting part!!! differ in the initial state C i C i+1 of a single process p S in S in Lemma 2 ● which p which p takes no takes no P has a bivalent initial configuration. ○ step step C/p Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... 0 differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  50. Most exciting part!!! differ in the initial state C i C i+1 of a single process p S in S in Lemma 2 ● which p which p takes no takes no P has a bivalent initial configuration. ○ step step C/p Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... 1 differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  51. 0/1 Most exciting part!!! differ in the initial state C i C i+1 of a single process p S in S in Lemma 2 ● which p which p takes no takes no P has a bivalent initial configuration. ○ step step C/p Assume all initial configurations are either 0-valent or 1-valent. Adjacent: ... ... 1 differ in the C 1 C 2 C i C i+1 C k initial state of a single process 0 0 0 1 1

  52. Proof Outline For any protocol, there is an initial configuration that is bivalent ● Then there is another bivalent configuration reachable from it after ● applying some event And another reachable bivalent configuration ● … ● An infinite undeciding run ●

  53. Most exciting part!!! Lemma 3 ● Let C be a bivalent configuration of P, and e=(p, m) be an event that is ○ applicable to C. Let E be the set of configurations reachable from C without applying e, and let D=e(E), the set of configurations after applying e to all those in E. Then, D contains a bivalent configuration.

  54. Most exciting part!!! Lemma 3 ● Let C be a bivalent configuration of P, and e=(p, m) be an event that is ○ applicable to C. Let E be the set of configurations reachable from C without applying e, and let D=e(E), the set of configurations after applying e to all those in E. Then, D contains a bivalent configuration. C 0/1

  55. Most exciting part!!! Lemma 3 ● Let C be a bivalent configuration of P, and e=(p, m) be an event that is ○ applicable to C. Let E be the set of configurations reachable from C without applying e, and let D=e(E), the set of configurations after applying e to all those in E. Then, D contains a bivalent configuration. Any schedule E 1 without C applying e E 2 E 3 ... 0/1 E

  56. Most exciting part!!! Lemma 3 ● Let C be a bivalent configuration of P, and e=(p, m) be an event that is ○ applicable to C. Let E be the set of configurations reachable from C without applying e, and let D=e(E), the set of configurations after applying e to all those in E. Then, D contains a bivalent configuration. Any schedule E 1 D 1 Apply e without C applying e E 2 D 2 E 3 D 3 ... ... 0/1 E D

  57. Most exciting part!!! Lemma 3 ● Let C be a bivalent configuration of P, and e=(p, m) be an event that is ○ applicable to C. Let E be the set of configurations reachable from C without applying e, and let D=e(E), the set of configurations after applying e to all those in E. Then, D contains a bivalent configuration. Any schedule E 1 D 1 Apply e without C applying e E 2 D 2 E 3 D 3 0/1 ... ... 0/1 E D

  58. Most exciting part!!! Assume all configurations in D are univalent. ●

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Circumventing Impossibility Partial Synchrony Circumventing Impossibility Consensus is an

Circumventing Impossibility Partial Synchrony Circumventing Impossibility Consensus is an

Circumventing Impossibility Partial Synchrony Circumventing Impossibility Consensus is an important building block for fault-tolerant computing Universal: any deterministic fault-tolerant service can be implemented on top of it

349 views • 12 slides
FLP Impossibility & Weakest Failure Detector Consensus Protocols in Theory Philip Daian -

FLP Impossibility & Weakest Failure Detector Consensus Protocols in Theory Philip Daian -

FLP Impossibility & Weakest Failure Detector Consensus Protocols in Theory Philip Daian - 10/25 slides influenced by Birman FA12 slides Consensus! Courtesy of https://rethinkdb.com Consensus Example Clients Storage Leader Consensus

1.53k views • 78 slides
1 What makes consensus hard? Fischer, Lynch and Patterson Fundamentally, the issue revolves

1 What makes consensus hard? Fischer, Lynch and Patterson Fundamentally, the issue revolves

Consensus a classic problem Consensus, impossibility Consensus abstraction underlies many results and Paxos distributed systems and protocols N processes They start execution with inputs { 0,1} Ken Birman Asynchronous,

255 views • 8 slides
Distributed Systems CS425/ECE428 03/06/2020 Todays agenda Consensus Consensus in

Distributed Systems CS425/ECE428 03/06/2020 Todays agenda Consensus Consensus in

Distributed Systems CS425/ECE428 03/06/2020 Todays agenda Consensus Consensus in synchronous systems Chapter 15.4 Impossibility of consensus in asynchronous systems Impossibility of Distributed Consensus with One Faulty

714 views • 40 slides
Consensus and Its Impossibility in Asynchronous Systems A Few Questions from Protocols We

Consensus and Its Impossibility in Asynchronous Systems A Few Questions from Protocols We

Consensus and Its Impossibility in Asynchronous Systems A Few Questions from Protocols We studied Was it necessary to assume that a node can detect failure of other nodes? What if we could not do that in a system? E.g., if delays

366 views • 22 slides
Consensus I FLP Impossibility, Paxos CS 240: Computing Systems and Concurrency Lecture 8 Marco

Consensus I FLP Impossibility, Paxos CS 240: Computing Systems and Concurrency Lecture 8 Marco

Consensus I FLP Impossibility, Paxos CS 240: Computing Systems and Concurrency Lecture 8 Marco Canini Credits: Michael Freedman and Kyle Jamieson developed much of the original material. Recall our 2PC commit problem Client C 1. C TC:

831 views • 46 slides
CS5412: CONSENSUS AND THE FLP IMPOSSIBILITY RESULT Lecture XII Ken Birman Generalizing Sam and

CS5412: CONSENSUS AND THE FLP IMPOSSIBILITY RESULT Lecture XII Ken Birman Generalizing Sam and

CS5412 Spring 2012 (Cloud Computing: Birman) 1 CS5412: CONSENSUS AND THE FLP IMPOSSIBILITY RESULT Lecture XII Ken Birman Generalizing Sam and Jills challenge 2 Recall from last time: Sam and Jill had difficulty agreeing where to meet

967 views • 42 slides
CONSENSUS Fall 2012 Ken Birman Consensus a classic problem Consensus abstraction underlies

CONSENSUS Fall 2012 Ken Birman Consensus a classic problem Consensus abstraction underlies

IMPOSSIBILITY OF CONSENSUS Fall 2012 Ken Birman Consensus a classic problem Consensus abstraction underlies many distributed systems and protocols N processes They start execution with inputs {0,1} Asynchronous,

511 views • 35 slides
CS5412: CONSENSUS AND THE FLP IMPOSSIBILITY RESULT Lecture XII Ken Birman Generalizing Ron and

CS5412: CONSENSUS AND THE FLP IMPOSSIBILITY RESULT Lecture XII Ken Birman Generalizing Ron and

CS5412 Spring 2016 (Cloud Computing: Birman) 1 CS5412: CONSENSUS AND THE FLP IMPOSSIBILITY RESULT Lecture XII Ken Birman Generalizing Ron and Hermiones challenge 2 Recall from last time: Ron and Hermione had difficulty agreeing where

975 views • 42 slides
Consensus and Dissent or: Meta - Consensus Consensus about what we have consensus

Consensus and Dissent or: Meta - Consensus Consensus about what we have consensus

Consensus and Dissent or: Meta - Consensus Consensus about what we have consensus on Building on Bitcoin Lisboa, Portugal -- 4 July 2018 Paul Sztorc Twitter: @truthcoin paul@tierion.com 16C8 1597 E76E 86E6 C01E F037 AA4B 3330

619 views • 37 slides
Consensus Building Consensus is Consensus is finding an acceptable proposal that all members

Consensus Building Consensus is Consensus is finding an acceptable proposal that all members

Consensus Building Consensus is Consensus is finding an acceptable proposal that all members can support. Consensus is not A unanimous vote A majority vote Everyone 100% satisfied Consensus requires Time Active

351 views • 7 slides
Distributed Algorithms (PhD course) Consensus SARDAR MUHAMMAD SULAMAN Consensus The

Distributed Algorithms (PhD course) Consensus SARDAR MUHAMMAD SULAMAN Consensus The

Distributed Algorithms (PhD course) Consensus SARDAR MUHAMMAD SULAMAN Consensus The processes use consensus to agree on a common value out of values they initially propose Reaching consensus is one of the most fundamental problems in

591 views • 38 slides
Outline Asynchronous shared memory model Wait-free Consensus in shared memory with R/W

Outline Asynchronous shared memory model Wait-free Consensus in shared memory with R/W

Shared Memory and Impossibility of Wait-Free Consensus Outline Asynchronous shared memory model Wait-free Consensus in shared memory with R/W variables Power of shared variables Wait-free Consensus hierarchy Shared Memory

572 views • 12 slides
When Aeron Met Raft Martin Thompson - @mjpt777 What does Consensus mean? consensus

When Aeron Met Raft Martin Thompson - @mjpt777 What does Consensus mean? consensus

Cluster Consensus When Aeron Met Raft Martin Thompson - @mjpt777 What does Consensus mean? consensus noun \ k n- sen(t)-s s \ : general agreement : unanimity Source: http://www.merriam-webster.com/ consensus noun \ k

1.14k views • 68 slides
The Impossibility of a Paretian Liberal Christian Geist Project: Modern Classics in Social Choice

The Impossibility of a Paretian Liberal Christian Geist Project: Modern Classics in Social Choice

The Author Setting, Definitions and Conditions Sen s Impossibility Theorem and Proof Critique and Ways Out Conclusion The Impossibility of a Paretian Liberal Christian Geist Project: Modern Classics in Social Choice Theory Institute

1.98k views • 15 slides
An Impossibility Theorem Seminar Algorithms Kevin Chang Eindhoven University of Technology June

An Impossibility Theorem Seminar Algorithms Kevin Chang Eindhoven University of Technology June

An Impossibility Theorem Seminar Algorithms Kevin Chang Eindhoven University of Technology June 19, 2018 Contents Motivation Definitions The Impossibility Theorem Centroid-Based Clustering and Consistency Relaxing the Properties Table of

1.08k views • 96 slides
GOAL S AND OBJE CT I VE S Assist Cha pla ins in b e c o ming mo re e ffe c tive ministe

GOAL S AND OBJE CT I VE S Assist Cha pla ins in b e c o ming mo re e ffe c tive ministe

4/4/2014 P A UL A N D ERSO N D IREC TO R GOAL S AND OBJE CT I VE S Assist Cha pla ins in b e c o ming mo re e ffe c tive ministe rs to individua ls a nd fa milie s Pre se nt ho w c ha ng e s in c ulture ha ve impa c te d pe

334 views • 7 slides
Announcements Meeting for business at the rise of meeting today June 18 Fathers Day

Announcements Meeting for business at the rise of meeting today June 18 Fathers Day

Announcements Meeting for business at the rise of meeting today June 18 Fathers Day celebration and Pot Luck June 25 Etching after meeting and Pizzas and Salad July 8 -- Youngs Dairy in Yellow Springs Young

452 views • 22 slides
Requirements Capture Roman Kontchakov Birkbeck, University of London Based on Chapter 6, 12 and

Requirements Capture Roman Kontchakov Birkbeck, University of London Based on Chapter 6, 12 and

Information Systems Concepts Requirements Capture Roman Kontchakov Birkbeck, University of London Based on Chapter 6, 12 and 21 of Bennett, McRobb and Farmer: Object Oriented Systems Analysis and Design Using UML, (4th Edition), McGraw Hill,

398 views • 27 slides
Jews Metropolitan Tel Aviv, with 2.5 million Jews, is the

Jews Metropolitan Tel Aviv, with 2.5 million Jews, is the

Jews Metropolitan Tel Aviv, with 2.5 million Jews, is the world's largest Jewish city. It is followed by New York, with 1.9 million , Haifa 655,000, Los Angeles 621,000, Jerusalem 570,000, and southeast Florida

367 views • 10 slides
Distributed Consensus: Making Impossible Possible Heidi Howard PhD Student @ University of

Distributed Consensus: Making Impossible Possible Heidi Howard PhD Student @ University of

Distributed Consensus: Making Impossible Possible Heidi Howard PhD Student @ University of Cambridge heidi.howard@cl.cam.ac.uk @heidiann360 hh360.user.srcf.net Sometimes inconsistency is not an option Distributed locking Financial

1.28k views • 74 slides
A Mean Field Games Approach to Consensus Problems Mojtaba Nourian McGill University, Montr

A Mean Field Games Approach to Consensus Problems Mojtaba Nourian McGill University, Montr

A Mean Field Games Approach to Consensus Problems Mojtaba Nourian McGill University, Montr eal, Canada Information and Control in Networks LCCC, Lunds University 23 October 2012 Joint work with Professors Peter Caines, Roland Malham e

557 views • 22 slides
Consensus and Agreement when Analyzing Qualitative Data Sheelagh Carpendale what is the goal?

Consensus and Agreement when Analyzing Qualitative Data Sheelagh Carpendale what is the goal?

Consensus and Agreement when Analyzing Qualitative Data Sheelagh Carpendale what is the goal? understand the real world a little better understand the real world a little better usually constrained to be about a very small part of the real

575 views • 11 slides
Pescara, Italy, July 2019 DIGRAPHS II Diffusion and Consensus on Digraphs Based on: [1]: J. S.

Pescara, Italy, July 2019 DIGRAPHS II Diffusion and Consensus on Digraphs Based on: [1]: J. S.

Pescara, Italy, July 2019 DIGRAPHS II Diffusion and Consensus on Digraphs Based on: [1]: J. S. Caughman 1 , J. J. P. Veerman 1 , Kernels of Directed Graph Laplacians , Electronic Journal of Combinatorics, 13, No 1, 2006. [2]: J. J. P. Veerman 1

591 views • 38 slides

More recommend