Re: [alto] Interop test
Wendy Roome <w.roome@...>
Interesting point! RFC 7285 does NOT require cost metrics -- numerical or ordinal -- to follow the requirements for a formal metric. Other than the values must be non-negative.
In particular, there is no requirement that d(x,x) = 0, or that d(x,y) = 0 iff x = y.
Costs are directed, so symmetry isn't even appropriate.
I guess I would expect a numeric metric to follow the triangle inequality, more or less, but there is no formal requirement for it do so.
Incidentally, for ordinal mode costs, the values are only comparable to other costs in the same request. In other words, if an ordinal cost in a filtered cost map is 0, that just means it is the lowest cost for the set of sources & destinations you requested. It is NOT the lowest cost for the full map.
- Wendy Roome
From: "Bertz, Lyle T [CTO]" <Lyle.T.Bertz@...>
Date: Fri, May 29, 2015 at 15:21
To: Wendy Roome <w.roome@...>, "Y. Richard Yang" <yry@...>
Cc: "alto@..." <alto@...>, Hans Seidel <hseidel@...>, "alto-dev@..." <alto-dev@...>
Subject: RE: [alto] Interop test
I have a much larger question about ordinal rank in 7285, is it the expectation that ordinal ranks are true metrics in practice. In other words are they or even the original metrics true mathematical metrics, i.e. non-negative, have symmetry, coincidence axiom and the triangle inequality. Further are they formally ultrametrics or intrinsic?
I only ask because depending on the answer we can add services for max distance, sum distance and the like that apply graph theory to the resulting maps. Who know, I may even be able to apply my only graph theories to them but I will keep such aspirations low at the moment.