1. 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?

  2. Is Barvinok's algorithm available online?

  • $\begingroup$ Is this a right forum for such sort questions? $\endgroup$ – user64494 Mar 18 '18 at 3:50
  • $\begingroup$ mathematical software is a tag. $\endgroup$ – T.... Mar 18 '18 at 5:40

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.

  • $\begingroup$ 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? $\endgroup$ – T.... Mar 18 '18 at 5:40
  • 2
    $\begingroup$ lattE implements more than that, in particular it can do ILP $\endgroup$ – Dima Pasechnik Mar 18 '18 at 9:44
  • $\begingroup$ @Turbo: The answer to your question may be in the paper I cited. Or you might write to DeLoera. $\endgroup$ – Joseph O'Rourke Mar 18 '18 at 11:44
  • $\begingroup$ @DimaPasechnik Does the software do Mixed ILP with Barvinok's algorithm? $\endgroup$ – T.... Apr 10 '18 at 11:56
  • $\begingroup$ 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. $\endgroup$ – Dima Pasechnik Apr 10 '18 at 17:36

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