       Re: Shortest Path Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg96394] Re: Shortest Path Problem
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 12 Feb 2009 06:43:18 -0500 (EST)
• References: <gmu8kl\$ggb\$1@smc.vnet.net>

```Hi,

you are wrong, the Combinatorica package may help, but you need
the

Needs["GraphUtilities`"]

package and the GraphPath[] function.

Regards
Jens

Antonio wrote:
> Dear Mathematica Users,
>
> I am not familiar with Graph theory and hope that some Mathematica
> users might help me. I am having a Shortest path problem that I hope
> to solve using Mathematica.
>
> My input is a Grid defind as,
>
> MyGrid = Table[RandomInteger[{1, 5}], {i, 1, 10}, {j, 1, 10}]
>
> in this 10x10 grid i'd like the shortest path from point A, let's say
> MyGrid[[10, 10]] to point B MyGrid[[1, 1]]. For every point inside
> this square grid I have 8 possible directions or lines
> (up,down,left,right and the 4 diagonals). The weight of each step is
> given inside the MyGrid cell, i.e. let MyGrid[[2, 3]]=1 and MyGrid[[2,
> 4]]=3
> So in going from coordinate (2,3) to (2,4) it takes 3 times as long as
> if going from (2,4) to (2,3). So all directions are possible but they
> are asymetrical in the sense that they have diferent weights if going
> foward or backward.
>
> I tried reading Mathematica help but it is very poor with no examples.
> All I know is that I have to use the Combinatorica package and the
> ShortestPath[] command, but as a start I have no idea in how to create
> a Graph needed as input to this command from MyGrid.
>