Petrozavodsk State University
Department of Computer Science

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Examples of ANLDE systems

Here is an example of a typical ANLDE system:

x1 + x2 = 2*x1 + 3*x3
x3 + x4 = x1 + 2*x2 + x3

If you process it with Process ANLDE system feature in the menu on the left of this page, then you see its Hilbert basis (minimal solutions), found by the syntactic algorithm:

h1 = (1,1,0,3) and h2 = (0,3,1,6)

The same result is given by the slopes algorithm (M.Filgueiras and A.-P.Tomas); this is an alternative solver, supported by Web-SynDic.

Thus, any solution of this ANLDE system has the form:

x = a*h1 + b*h2 for nonnegative integer a and b

Using the cost function

x1 + x2 + x3 + x4 -> min

one can solve the optimization problem with this cost function and the considered ANLDE system as constraints and get one particular solution of the ANLDE system by standard integer programming methods:

x = (1,1,0,3)

The optimal solution is always equal to an element of the Hilbert basis.

As ILP solver we use lp_solve (M.Berkelaar) - another alternative solver, supported by Web-SynDic. This solver is based on the well-known technique of simplex algorithm among with branch-and-bound method.

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