[boost] [graph] Proposal: Algorithm for the Shortest Path Problem with Resource Constraints

From: Michael Drexl (michael_at_[hidden])
Date: 2005-12-06 13:59:26

Hi,

is there any interest in including an algorithm for solving the shortest 
path problem with resource constraints (SPPRC) in the Boost Graph library?

I've implemented an exact algorithm for this NP-hard problem. The 
algorithm is basically a label-setting algorithm based on dynamic 
programming. It is parameterized on the graph type (of course) and the 
type of the resource container (data structures specifying what 
resources there are and how they are to be managed in the course of the 
algorithm).

Some remarks on the underlying problem:
The SPPRC seeks the shortest (fastest, cheapest) path in a network with 
arbitrary arc lengths (travel times, costs) from an origin node to a 
destination node subject to one or more resource constraints. For 
example, one might seek a path of minimum length from o to d subject to 
the constraints that
- the total travel time must not exceed some upper bound and/or
- the total amount of some good that has to be picked up at the vertices 
along the path be less than or equal to some capacity limit and/or
- if two vertices i_1 and i_2 are visited on a path, then i_1 must be 
visited before i_2
- etc.

The problem is NP-hard in the strong sense. If the path need not be 
elementary, i.e., if it is allowed that vertices or arcs are visited 
more than once, the problem can be solved in pseudopolynomial time.

A recent survey on the problem is:
Desaulniers, G.; Irnich, S. (2005):
Shortest Path Problems with Resource Constraints
in:
Desaulniers, G.; Desrosiers, J.; Solomon, M. (eds.) (2005):
Column Generation
Springer, New York, pp. 33--65

(available online via
www.dpor.rwth-aachen.de/de/publikationen/pdf/or_2004-01.pdf)

Regards,

Michael D.