Talk:Criss-cross algorithm

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Computer science Low‑importance

This article is within the scope of WikiProject Computer science, a collaborative effort to improve the coverage of Computer science related articles on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.Computer scienceWikipedia:WikiProject Computer scienceTemplate:WikiProject Computer scienceComputer science articles

Low

This article has been rated as Low-importance on the project's importance scale.

Things you can help WikiProject Computer science with:

Here are some tasks awaiting attention:

Article requests :
- Requested articles/Applied arts and sciences/Computer science, computing, and Internet
Cleanup :
- Computer science articles needing attention
- Computer science articles needing expert attention
Copyedit :
- Computing
Expand :
- Computer science
Infobox :
- Computer science articles without infoboxes
Maintain :
- Timeline of computing 2020–present
Photo :
- Find pictures for the biographies of computer scientists (see List of computer scientists)
- Computing articles needing images
Stubs :
- Computer science stubs
Unreferenced :
- WikiProject Computer science/Unreferenced BLPs
Project-related :
- Tag all relevant articles in Category:Computer science and sub-categories with {{WikiProject Computer science}}

Systems Low‑importance

	Systems science portal This article is within the scope of WikiProject Systems, which collaborates on articles related to systems and systems science.SystemsWikipedia:WikiProject SystemsTemplate:WikiProject SystemsSystems articles
Low	This article has been rated as Low-importance on the project's importance scale.
	This article is within the field of Operations research.

A fact from Criss-cross algorithm appeared on Wikipedia's Main Page in the Did you know column on 5 April 2011 (check views). The text of the entry was as follows:

Did you know... that, while the criss-cross algorithm visits all eight corners of the Klee–Minty cube when started at a worst corner, it visits only three more corners on average when started at a random corner?

A record of the entry may be seen at Wikipedia:Recent additions/2011/April.

Wikipedia

Did You Know?

Old nomination: Inaccessible

I nominated the following hook: Kiefer.Wolfowitz (Discussion) 00:57, 22 March 2011 (UTC)[reply]

Did you know ... that the criss-cross algorithm' and the simplex algorithm are not polynomial-time algorithms because they visit all 2^D corners of a cube in dimension D?

That sounds a bit difficult for a DYK, don't you think? I mean, is there any way it could be worded to be more accessible? CRGreathouse (t | c) 04:25, 22 March 2011 (UTC)[reply]

In particular, I don't think many readers—even mathematically sophisticated ones—will know of the Klee–Minty cube, nor the significance of a vector space's dimension. If I were writing it (and I'm not!) I might say something about the fact that it's an exponential-time algorithm that performs far better in practice. Surely there are other things that educated but nonspecialist readers could appreciate? CRGreathouse (t | c) 19:50, 22 March 2011 (UTC)[reply]

That's helpful. At least the phrase "Klee-Minty" should go!

Caveat: I have not yet provided a reference to the expected behavior of the criss cross algorithm (which is D on cubes of dimension D, I believe). The expected number of steps of the simplex algorithm is also linear under a wide class of models (which are incompatible with reality, alas); the expected running time is usually thought to be about 3D on practical problems.

I simplified it a bit. Kiefer.Wolfowitz (Discussion) 19:59, 22 March 2011 (UTC)[reply]

New hook: Accessible

Maybe this would work better?

- Did you know ... that the criss-cross algorithm and the simplex algorithm can visit all 2^D corners of a cube in dimension D but visit only D corners on average?

If you like this, then I should find a reference. Best regards, Kiefer.Wolfowitz (Discussion) 20:04, 22 March 2011 (UTC)[reply]

I added some preliminary referencing about average behavior. The expected behavior of the simplex method (on problems from the unit sphere) is O(D) by Borgwardt and Smale. I don't have Klee & Minty's paper handy, but it seems trivial that a cube drawn from the sphere should have D steps on average. (I don't have time to reference properly today: Iterating the bibliography operator initialized with Fukuda & Terlaky should suffice. Sincerely, Kiefer.Wolfowitz (Discussion) 20:25, 22 March 2011 (UTC)[reply]

I nominated the alternative. Thanks for the suggestions. Kiefer.Wolfowitz (Discussion) 21:06, 22 March 2011 (UTC)[reply]

Looks good to me. CRGreathouse (t | c) 23:25, 22 March 2011 (UTC)[reply]

I submitted it, along with a graphic. Please consider vetting it at DYK. Thanks again for your feedback. (I evaluated the D and 2^D expressions with D=3, computing 3 and 8 respectively: I trust this does not violate Original Research policy!) Cheers, Kiefer.Wolfowitz (Discussion) 00:40, 23 March 2011 (UTC)[reply]

DYK: The article was viewed 4536 times in 201104. Kiefer.Wolfowitz (Discussion) 00:29, 6 April 2011 (UTC)[reply]

Example or Illustration needed

The article needs an example, preferably with an illustration, to move up to "B class". Kiefer.Wolfowitz 22:35, 30 August 2011 (UTC)[reply]