[R-sig-Geo] Distances in shortestPath function (package spatgraphs)

[Tuomas Rajala]

Dear Julian,

the algorithm finds the shortest paths in a weighted graph with each
edge weight being the Euclidian distance between corresponding node
locations. Weights are constant 1 if 'pp', and hence the node
locations, are not provided. For reference, see e.g.
http://en.wikipedia.org/wiki/Dijkstra's_algorithm

So, if
1. you give pp, the edges are weighted with Euclidian distances, and
the result is the geographical minimum distance needed to travel along
the graph from i to j,

2. you don't give pp, in which case each edge has weight 1, and the
result is the shortest path in term of edges needed to hop to get from
i to j.

To answer your question: Shortest path in terms of distance is given
by 1., and in term of nodes given by 2.

Sorry for the mix-up in terms: General graph term for the cost of
traveling each edge is 'weight'; I use 'length' in the docs, as it
makes sense in spatial context.

Hope this helps,
Tuomas R



2012/6/18 Julian Burgos <julian at hafro.is>
>
> Dear list,
>
> I have a question about the shortestPath function (in the package
> spatgraphs... a very useful package but with very sparse documentation).
>  The function finds the shortest connection between two nodes in a graph.
>  According to the documentation, the usage of the function is
>
> shortestPath(i, j, g, pp=NULL, dbg=FALSE)
>
> where i and j are the starting and ending nodes, g is the graph that
> defines de edges, and pp is a point pattern.  If pp is given, "the edges are
> of Euclidian length, otherwise each edge is of length 1.".
>
> So this is my question:  if I give a point pattern, does the shortesPath
> function finds the shortest path in terms of distances between nodes or in
> terms of number of nodes?  In other words, will the algorithm select a
> shorter path in terms of distance even if it goes through a larger number of
> nodes?  I am asking because my graph  is very dense (has lots of points) in
> some areas, and it is very sparse in others.  I want to make sure that the
> algorithm actually picks the track with the shortest distance and not the
> track with the lowest number of nodes.
> Thanks!
>
> Julian
>
> --
> Julian Mariano Burgos, PhD
> Hafrannsóknastofnunin/Marine Research Institute
> Skúlagata 4, 121 Reykjavík, Iceland
> Sími/Telephone : +354-5752037
> Bréfsími/Telefax:  +354-5752001
> Netfang/Email: julian at hafro.is
>