Re: Canonical DB
From: mAsterdam <mAsterdam_at_vrijdag.org>
Date: Sat, 24 Jun 2006 13:02:42 +0200
Message-ID: <449d1b74$0$31641$e4fe514c_at_news.xs4all.nl>
>
> 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).
Date: Sat, 24 Jun 2006 13:02:42 +0200
Message-ID: <449d1b74$0$31641$e4fe514c_at_news.xs4all.nl>
Dmitry A. Kazakov wrote:
> Gene Wirchenko wrote:
>> Dmitry A. Kazakov wrote: >>> 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).
W = {Mon, Tue, Wed, Thu, Fri, Sat, Sun}
d(Mon, Fri) = 4
d(Fri, Mon) = 3
> 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.
Which is not always the sensible thing to do.
-- "The person who says it cannot be done should not interrupt the person doing it." Chinese Proverb.Received on Sat Jun 24 2006 - 13:02:42 CEST