  We present a new algorithm for computing a truncated Markov basis of a
lattice. In general, this new algorithm is faster than existing methods. We
then extend this new algorithm so that it solves the linear integer feasibility
problem with promising results for equality knapsack problems. We also present
a novel Groebner basis approach to solve a particular integer linear program as
opposed to previous Groebner basis methods that effectively solved many
different integer linear programs simultaneously. Initial results indicate that
this optimisation algorithm performs better than previous Groebner basis
methods.

Optimization and Control;Combinatorics