Re: [boost] BGL: traveling sales man

From: Steve Nutt (Steve.Nutt_at_[hidden])
Date: 2007-10-23 21:14:36

It would be great if this also worked with spherical geometry as well!

-----Original Message-----
From: Douglas Gregor [mailto:dgregor_at_[hidden]] 
Sent: Tuesday, October 23, 2007 9:34 AM
To: boost_at_[hidden]
Subject: Re: [boost] BGL: traveling sales man

Michael Held wrote:
> Hi Doug,
>
> Yhank you very much. Your reply was *very* helpful and the code worked
> out of the box.
>
> What should be done to bring TSP closer to boost?
>   
A couple things I saw:
  - Needs documentation!
  - Test driver needs to validate its result, not just print it
  - It would be nice if we had the 1.5x approximation rather than the 2x

approximation, of course...
  - The algorithm should accept a function object that computes the 
distance between two vertices in the graph; of course, that function 
object needs to satisfy the triangle equality, and should default to 
Euclidean distance, but it's good to have that customizability
  - We shouldn't be building the first graph (the complete graph) in 
memory, ever. Ideally, we would create an implicit-graph type that 
enumerates edges on-the-fly. Or, if we really need to create the graph, 
why not use adjacency_matrix instead of adjacency_list?
  - The Tour parameter should be an OutputIterator, not an array, to 
better match the interfaces in the rest of the BGL.
  - I would have expected the TSP-2 approximation algorithm to accept a 
graph, but it doesn't; instead, it infers the number of vertices from 
the "size" of the property map. Unfortunately, there is no such notion 
for property maps, so the PositionMap is essentially restricted to a 
vector_property_map. I'd rather have the algorithm accept a 
VertexListGraph, then compute the TSP-2 approximation for that graph 
based on just a distance function between two vertices.

IMO, the signature of the algorithm should be:

    template<typename VertexListGraph, typename DistanceFunction, 
typename OutputIterator>
    OutputIterator tsp_2_approximation(VertexListGraph const& g, 
DistanceFunction distance, OutputIterator out);

For the normal case of Euclidian distance, one would provide a function 
template that turns a PositionMap into a distance function:
   
    template<typename PositionMap>
    ??? euclidean_distance(PositionMap position);
> So far the TSP approximation of a list of 2D points is straight
forward
> implemented (using the Euclidean distance between each pair of points
as
> edge weight). I guess this needs to be generalized for a boost
integration.
> But I would like to include his 'tsp_2_approximation' shortcut, as it
> solves the probably most common TSP problem: return the tour indices
for
> a given list of points...
>   
Sure, it's always good to have shortcut algorithm for the simplest
cases.

    - Doug
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