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. >