Re: Canonical DB

From: Dmitry A. Kazakov <mailbox_at_dmitry-kazakov.de>
Date: Sat, 24 Jun 2006 10:58:36 +0200
Message-ID: <4lsoa08lt2qu$.1mefkf7jftxz4$.dlg@40tude.net>

On Fri, 23 Jun 2006 15:51:07 -0700, Gene Wirchenko wrote:

> On Fri, 23 Jun 2006 21:59:52 +0200, "Dmitry A. Kazakov"
> <mailbox_at_dmitry-kazakov.de> wrote:
>

>>On Fri, 23 Jun 2006 15:37:54 +0200, mAsterdam wrote:

>

>>> These requirements establish K as a clean point type.
>>> Aside: With the last condition deleted one can make a
>>> circular K, having distance(k1, k2) <> distance(k2, k1).
>>
>>That won't be formally a distance, which is required to be symmetric.


> 

>      Why must it be symmetric?  A to B and B to A may be different

> distances if there are one-way routes involved.

Rather when the space is anisotropic. If you just have many routes, you still could get a metric distance by choosing the shortest path.

---

I found in Wikipedia that d(x,y) /= d(y,x) is called quasimetric space (I never met such thing anywhere else). Wikipedia also states that any quasimetric space can be made metric, by defining

   d*(x,y) = (d(x,y) + d(y,x)) / 2

So it can be made metric.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de

Received on Sat Jun 24 2006 - 03:58:36 CDT