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D.4.9.1 solve_IP
Procedure from library intprog.lib (see intprog_lib).
- Usage:
- solve_IP(A,bx,c,alg); A intmat, bx intvec, c intvec, alg string.
solve_IP(A,bx,c,alg); A intmat, bx list of intvec, c intvec,
alg string.
solve_IP(A,bx,c,alg,prsv); A intmat, bx intvec, c intvec,
alg string, prsv intvec.
solve_IP(A,bx,c,alg,prsv); A intmat, bx list of intvec, c intvec,
alg string, prsv intvec.
- Return:
- same type as bx: solution of the associated integer programming
problem(s) as explained in
Toric ideals and integer programming.
- Note:
- This procedure returns the solution(s) of the given IP-problem(s)
or the message `not solvable'.
One may call the procedure with several different algorithms:
- the algorithm of Conti/Traverso (ct),
- the positive variant of the algorithm of Conti/Traverso (pct),
- the algorithm of Conti/Traverso using elimination (ect),
- the algorithm of Pottier (pt),
- an algorithm of Bigatti/La Scala/Robbiano (blr),
- the algorithm of Hosten/Sturmfels (hs),
- the algorithm of DiBiase/Urbanke (du).
The argument `alg' should be the abbreviation for an algorithm as
above: ct, pct, ect, pt, blr, hs or du.
`ct' allows computation of an optimal solution of the IP-problem
directly from the right-hand vector b.
The same is true for its `positive' variant `pct' which may only be
applied if A and b have nonnegative entries.
All other algorithms need initial solutions of the IP-problem.
If `alg' is chosen to be `ct' or `pct', bx is read as the right hand
vector b of the system Ax=b. b should then be an intvec of size m
where m is the number of rows of A.
Furthermore, bx and A should be nonnegative if `pct' is used.
If `alg' is chosen to be `ect',`pt',`blr',`hs' or `du',
bx is read as an initial solution x of the system Ax=b.
bx should then be a nonnegative intvec of size n where n is the
number of columns of A.
If `alg' is chosen to be `blr' or `hs', the algorithm needs a vector
with positive coefficients in the row space of A.
If no row of A contains only positive entries, one has to use the
versions of solve_IP which take such a vector prsv as an argument.
solve_IP may also be called with a list bx of intvecs instead of a
single intvec.
Example:
See also:
Integer programming;
intprog_lib;
toric_lib.
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