Channels ▼


The Byzantine Generals Problem

Source Code Accompanies This Article. Download It Now.

The Lamport, Pease, and Shostak Algorithm

In 1982, Lamport, Pease, and Shostak published a straightforward solution to this problem ( lamport/pubs/byz.pdf). The algorithm assumes that there are n processes, with m faulty processes, where n>3m. Thus, for a scenario such as that in Figures 1 and 2 with one faulty process, there would have to be a minimum of four processes in the system to come to agreement. (For purposes here, n refers to the count of processes, and m to the number of faulty processes.)

The definition of the algorithm in the original paper is short and succinct, but can be confusing for programmers who don't have experience with distributed algorithms.

Lamport's algorithm is a recursive definition, with a base case for m=0, and a recursive step for m>0:

  • r Algorithm OM(0)
  • The general sends his value to every lieutenant.
  • Each lieutenant uses the value he receives from the general.
  • r Algorithm OM(m), m>0
  • The general sends his value to each lieutenant.
  • For each i, let vi be the value lieutenant i receives from the general. Lieutenant i acts as the general in Algorithm OM(m-1) to send the value vi to each of the n-2 other lieutenants.
  • For each i, and each j i, let vi be the value lieutenant i received from lieutenant j in step 2 (using Algorithm (m-1)). Lieutenant i uses the value majority(v1, v2,

Lamport's Algorithm Definition

To most programmers, this is going to look like a conventional recursive function definition. However, it doesn't quite fit into the conventional recursive function mold you learned when studying the example of factorial(n).

Lamport's algorithm actually works in two stages. In the first step, the processes iterate through m+1 rounds of messages. In the second stage of the algorithm, each process takes all the information it has been given and uses it to come up with its decision.

Related Reading

More Insights

Currently we allow the following HTML tags in comments:

Single tags

These tags can be used alone and don't need an ending tag.

<br> Defines a single line break

<hr> Defines a horizontal line

Matching tags

These require an ending tag - e.g. <i>italic text</i>

<a> Defines an anchor

<b> Defines bold text

<big> Defines big text

<blockquote> Defines a long quotation

<caption> Defines a table caption

<cite> Defines a citation

<code> Defines computer code text

<em> Defines emphasized text

<fieldset> Defines a border around elements in a form

<h1> This is heading 1

<h2> This is heading 2

<h3> This is heading 3

<h4> This is heading 4

<h5> This is heading 5

<h6> This is heading 6

<i> Defines italic text

<p> Defines a paragraph

<pre> Defines preformatted text

<q> Defines a short quotation

<samp> Defines sample computer code text

<small> Defines small text

<span> Defines a section in a document

<s> Defines strikethrough text

<strike> Defines strikethrough text

<strong> Defines strong text

<sub> Defines subscripted text

<sup> Defines superscripted text

<u> Defines underlined text

Dr. Dobb's encourages readers to engage in spirited, healthy debate, including taking us to task. However, Dr. Dobb's moderates all comments posted to our site, and reserves the right to modify or remove any content that it determines to be derogatory, offensive, inflammatory, vulgar, irrelevant/off-topic, racist or obvious marketing or spam. Dr. Dobb's further reserves the right to disable the profile of any commenter participating in said activities.

Disqus Tips To upload an avatar photo, first complete your Disqus profile. | View the list of supported HTML tags you can use to style comments. | Please read our commenting policy.