lp_solve is a free linear programming and integer programming solver.  The
library is written in C, but the developers provide bindings to several
languages, including Python.

I have created an spkg for installing lp_solve into Sage.  The spkg is
located at:
http://www.math.unl.edu/~shartke2/files/

There is also a demo file domination.py that shows how to use the IP solver
to determine the domination number of a graph.  Once I figure out how to run
doctests (When I run sage -t domination.py, Python reports that module
domination cannot be found), I'll submit that file for inclusion in Sage as
well. Should domination.py be in the lp_solve spkg, or separate?

lp_solve has fewer features than GLPK (the GNU Linear Programming Kit), but
I've found that it's usually about as fast as GLPK.  Both of the
publicly-available Python bindings for GLPK are being updated to match the
latest version of GLPK; I hope to release an spkg for GLPK when they
stabilize.  Neither lp_solve nor GLPK is as powerful as the COIN-OR
software, but COIN is significantly more difficult to use.  Additionally,
GPLK is GPLv3 and COIN has some funky GPL-but-with-New-York-courts license,
so their inclusion in Sage may be problematic.  lp_solve is GPLv2.1.

Best wishes,
Stephen

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