Reducing the size and number of linear programs in a dynamic Gr\"obner   basis algorithm
  The dynamic algorithm to compute a Gr\"obner basis is nearly twenty years old, yet it seems to have arrived stillborn; aside from two initial publications, there have been no published followups. One reason for this may be that, at first glance, the added overhead seems to outweigh the benefit; the algorithm must solve many linear programs with many linear constraints. This paper describes two methods of reducing the cost substantially, answering the problem effectively. 
Massimo Caboara and John Perry
math.AC cs.SC