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Re: Shortest Path Problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg96395] Re: Shortest Path Problem
*From*: dh <dh at metrohm.com>
*Date*: Thu, 12 Feb 2009 06:43:29 -0500 (EST)
*References*: <gmu8kl$ggb$1@smc.vnet.net>
Hi Antonio,
assume we have a weight matrix w. From w we create a graph: g. We then
serach the shortest path from vertex 1 to 4. Finally we display the
costs of all shortest paths:
w = {{3, 7, 2, 6}, {7, 9, 3, 1}, {3, 2, 7, 6}, {9, 3, 6, 10}};
g = FromAdjacencyMatrix[w, EdgeWeight, Type -> Directed];
ShortestPath[g, 1, 4 ]
AllPairsShortestPath[g]
hope this helps, Daniel
ntonio 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.
>
> Thanks in advanced.
>
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