Choose columns so non-zero elements are first m entries in
where is .
Simplex method is a strategy for moving from one solution
to another
by changing one column of to
another that is not being used.
There is another class of methods---associated with Karmarkar at AT
and T which are so called interior point methods. That is, you do not
go from vertex to vertex of simplex but rather wander around inside
simplex. Both simplex and interior point methods are important.
.
is 
matrix. Usually r>> m.
is 
.
to another 
by changing one column of 
to
another that is not being used.