Comments on: Szemeredi’s regularity lemma via random partitions

By: The spectral proof of the Szemeredi regularity lemma « What’s new

The spectral proof of the Szemeredi regularity lemma « What’s new — Tue, 04 Dec 2012 01:35:44 +0000

[...] proofs of this lemma, which is actually not that difficult to establish; see for instance these previous blog posts for some examples. In this post I would like to record one further proof, based on the [...]

By: Szemerédi’s regularity lemma « Disquisitiones Mathematicae

Szemerédi’s regularity lemma « Disquisitiones Mathematicae — Sat, 24 Dec 2011 19:31:39 +0000

[...] the book The probabilistic method of Alon and Spencer, the survey of Komlós and M. Simonovits and Tao’s perspective via random partitions. Merry Christmas!! Share this:TwitterLike this:LikeBe the first to like this [...]

By: Moser’s entropy compression argument « What’s new

Moser’s entropy compression argument « What’s new — Thu, 06 Aug 2009 01:17:35 +0000

[...] is often referred to as the “index”). These examples are related; see this blog post for further discussion. The general strategy here is to keep looking for useful pieces of energy [...]

By: Szemeredi’s regularity lemma via the correspondence principle « What’s new

Sat, 09 May 2009 04:14:17 +0000

[...] math.PR | Tags: correspondence principle, szemeredi regularity lemma | by Terence Tao In a previous post, we discussed the Szemerédi regularity lemma, and how a given graph could be regularised by [...]

By: Anup

Anup — Tue, 28 Apr 2009 04:11:09 +0000

Hi Terry, for Lemma 2, do you want to allow i=j in the sum?

Otherwise it seems that partitioning the graph into one part V1 = V, would trivially satisfy the conclusions of the lemma.

[Hmm, you're right. Thanks for the correction! - T.]

By: Terence Tao

Terence Tao — Mon, 27 Apr 2009 18:31:43 +0000

Dear Asaf: thanks for the reference! It again seems to be slightly different from the random neighbourhoods algorithm (which is a O(1) algorithm rather than O(n), but only defines the partition implicitly and does not make it equitable) but certainly in the same spirit.

By: Asaf

Asaf — Mon, 27 Apr 2009 17:09:35 +0000

Hi Terry,

Such an O(n) algorithm appears (explicitly) in the following paper of mine with Fischer and Matsliach.

http://www.cs.tau.ac.il/~asafico/regalg.pdf

That algorithm actually has the added advantage of being able to find (more or less) the smallest regular partition in the input.