Talk:Criss-cross algorithm

Mathematics Start‑class Mid‑priority

	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
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Mid	This article has been rated as Mid-priority on the project's priority scale.

Computer science Start‑class Mid‑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

Start

This article has been rated as Start-class on Wikipedia's content assessment scale.

Mid

This article has been rated as Mid-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: Operations research Start‑class Mid‑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
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Mid	This article has been rated as Mid-importance on the project's importance scale.
	This article is within the field of Operations research.

Did You Know?

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]

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]