From: Jacob Fugal <lukfugl@...>
Date: 2005-05-10T08:30:11+09:00
Subject: Re: Representing Undirected Edges (advice, please)

On 5/9/05, Nuralanur@aol.com <Nuralanur@aol.com> wrote:
> But what if in your example you come up with three different incidence
> matrices connecting all pairs of nodes (i,j) , the first representing
> connection values with respect to Q, the second S, the third E,
> respectively?

I think you misunderstood. The three paths weren't one each for each
criterion. There were three distinct paths (or as Gavin suggested as
an alternate example, three distinct songs connecting two letters).
Each path then had three weights, one for each criterion. A Quickness
incidence matrix would still need to store (somehow) 3 values, one for
each of the edges connecting A and B.

> I feel that it is necessary to avoid evaluating n^d ( n-number of paths, d-
> dimension of criteria) items in searching for an optimal path ...

You don't need to evaluate them, unless you want to consider all
criteria at once. Usually you'd only choose one criterion. A
pathfinder which only cares about one criterion only needs to evaluate
one value from each of n paths. With incidence matrices you'd only
select one matrix (that corresponding to the chosen criterion) and
have n evaluations. Same boat.

The difference isn't in the number of criteria -- that was just an
illustrative concept. I admit my approach to the criteria may have
been simplistic (or even incorrect).

> Best regards,
> 
> Axel

Thanks for the feedback, Axel :)

Jacob Fugal