In 'Computational Experience with Lenstra's Algorithm' by L Gao, Y Zhang it is claimed that they have an implementation of Lenstra's fixed dimension integer programming algorithm. Is this available online anywhere?
Is Barvinok's algorithm available online?
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$\begingroup$ Is this a right forum for such sort questions? $\endgroup$– user64494Mar 18, 2018 at 3:50
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$\begingroup$ mathematical software is a tag. $\endgroup$– TurboMar 18, 2018 at 5:40
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This may be of some help:
De Loera, Jesús A., David Haws, Raymond Hemmecke, Peter Huggins, and Ruriko Yoshida. "A computational study of integer programming algorithms based on Barvinok's rational functions." Discrete Optimization 2, no. 2 (2005): 135-144. (Elsevier link.)
For their comparisons, they used the CPLEX MIP solver,
and the software package LattE
available at https://www.math.ucdavis.edu/~latte/software.php.
answered Mar 18, 2018 at 0:37
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$\begingroup$ I think it will help. So lattE implements Barvinok's algorithm? In spirit it has at least the same power as Lenstra's. Do you know what the complexity of Barvinok's algorithm is when employed for fixed dimension linear integer programming? $\endgroup$– TurboMar 18, 2018 at 5:40
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2$\begingroup$ lattE implements more than that, in particular it can do ILP $\endgroup$ Mar 18, 2018 at 9:44
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$\begingroup$ @Turbo: The answer to your question may be in the paper I cited. Or you might write to DeLoera. $\endgroup$ Mar 18, 2018 at 11:44
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$\begingroup$ @DimaPasechnik Does the software do Mixed ILP with Barvinok's algorithm? $\endgroup$– TurboApr 10, 2018 at 11:56
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$\begingroup$ It does ILP, see p.30 of the manual: math.ucdavis.edu/~latte/software/packages/latte_current/… It does not do Mixed ILP, only "pure" ILP. $\endgroup$ Apr 10, 2018 at 17:36