Chapter14 - Chapter 14: Consensus and Agreement Ajay...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 14: Consensus and Agreement Ajay Kshemkalyani and Mukesh Singhal Distributed Computing: Principles, Algorithms, and Systems Cambridge University Press Consensus and Agreement CUP 2008 1 / 54
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Distributed Computing: Principles, Algorithms, and Systems Assumptions System assumptions Failure models Synchronous/ Asynchronous communication Network connectivity Sender identification Channel reliability Authenticated vs. non-authenticated messages Agreement variable 0 G1 G2 G3 G4 0 1 1 1 0 0 1 0 0 0 1 Consensus and Agreement CUP 2008 2 / 54
Background image of page 2
Distributed Computing: Principles, Algorithms, and Systems Problem Specifications Byzantine Agreement (single source has an initial value) Agreement: All non-faulty processes must agree on the same value. Validity: If the source process is non-faulty, then the agreed upon value by all the non-faulty processes must be the same as the initial value of the source. Termination: Each non-faulty process must eventually decide on a value. Consensus Problem (all processes have an initial value) Agreement: All non-faulty processes must agree on the same (single) value. Validity: If all the non-faulty processes have the same initial value, then the agreed upon value by all the non-faulty processes must be that same value. Termination: Each non-faulty process must eventually decide on a value. Interactive Consistency (all processes have an initial value) Agreement: All non-faulty processes must agree on the same array of values A [ v 1 . . . vn ]. Validity: If process i is non-faulty and its initial value is v i , then all non-faulty processes agree on v i as the i th element of the array A . If process j is faulty, then the non-faulty processes can agree on any value for A [ j ]. Termination: Each non-faulty process must eventually decide on the array A . These problems are equivalent to one another! Show using reductions. Consensus and Agreement CUP 2008 3 / 54
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Distributed Computing: Principles, Algorithms, and Systems Overview of Results Failure Synchronous system Asynchronous system mode (message-passing and shared memory) (message-passing and shared memory) No agreement attainable; agreement attainable; failure common knowledge also attainable concurrent common knowledge attainable Crash agreement attainable agreement not attainable failure f < n Byzantine processes Ω( f + 1) rounds Byzantine agreement attainable agreement not attainable failure f ≤ b ( n - 1) / 3 c Byzantine processes Ω( f + 1) rounds Table: Overview of results on agreement. f denotes number of failure-prone processes. n is the total number of processes. In a failure-free system, consensus can be attained in a straightforward manner Consensus and Agreement CUP 2008 4 / 54
Background image of page 4
Distributed Computing: Principles, Algorithms, and Systems Some Solvable Variants of the Consensus Problem in Async Systems Solvable Failure model and overhead Definition Variants Reliable crash failures, n > f (MP) Validity, Agreement, Integrity conditions broadcast k -set crash failures. f < k < n . size of the set of values agreed consensus (MP and SM) upon must be less than k ± -agreement crash failures
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/23/2012 for the course COMP 553 taught by Professor Ajay during the Spring '12 term at Ill. Chicago.

Page1 / 55

Chapter14 - Chapter 14: Consensus and Agreement Ajay...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online