document: Minimised geometric Buchberger algorithm for integer programming Recently , various algebraic integer programming -LRB- IP -RRB- solvers have been proposed based on the theory of Grobner bases . The main difficulty of these solvers is the size of the Grobner bases generated . In algorithms proposed so far , large Grobner bases are generated by either introducing additional variables or by considering the generic IP problem IP/sub A , C / . Some improvements have been proposed such as Hosten and Sturmfels ' method -LRB- GRIN -RRB- designed to avoid additional variables and Thomas ' truncated Grobner basis method which computes the reduced Grobner basis for a specific IP problem IP/sub A , C / -LRB- b -RRB- -LRB- rather than its generalisation IPA , C -RRB- . In this paper we propose a new algebraic algorithm for solving IP problems . The new algorithm , called Minimised Geometric Buchberger Algorithm , combines Hosten and Sturmfels ' GRIN and Thomas ' truncated Grobner basis method to compute the fundamental segments of an IP problem IP/sub A , C / directly in its original space and also the truncated Grobner basis for a specific IP problem IP/sub A , C / -LRB- b -RRB- . We have carried out experiments to compare this algorithm with others such as the geometric Buchberger algorithm , the truncated geometric Buchberger algorithm and the algorithm in GRIN . These experiments show that the new algorithm offers significant performance improvement
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