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| GeoCommunity Mailing List |
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| Subject: | RE: [gislist] spatial question - put your thinking caps on |
| Date: |
11/26/2003 05:10:01 PM |
| From: |
Dimitri Rotow |
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|
>
> Not directly a GIS question, but as a spatially-enabled group, I'm
> hoping someone here can offer some pointers.
>
> I have a set of points with a known density. If I double the density,
> will I increase the distance incurred to travel to all the points? What
> will be the mathematical relationship between average distance between
> points (or the sum thereof) and their density?
>
> Of course I realize there are a lot of factors, not least of which will
> be the pattern of distribution and the pattern of road networks, but can
> I generalize in some fashion?
>
If you are routing over a road network, there is no generalization possible
for an optimal route to visit all points that does not take into account the
characteristics of the network and the distribution of the points. Let me
give you an example. Suppose you have a road network that consists of
straight links between nodes. Your first task is to visit all the nodes.
Let's say you compute the optimal route to visit all the nodes. That route
will traverse some of the links, perhaps very many of them. Now, let's say
you add an additional point to visit at the midpoint of all the links that
were traversed by the first solution. You might end up ending very many
additional points to visit (thus greatly increasing the density of points)
but you will not increase the length of the optimal route at all because
every point that was added already lies on a link that is being traversed.
The usual approach in practical situations is not to find a mathematical
solution but to try out different test cases using GIS software that can
quickly and easily tell you what the optimal route is. For an example of
such usage, see
http://exchange.manifold.net/manifold/manuals/5_userman/mfd50Optimal_Route_V
isual.htm
Cheers,
Dimitri
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