We investigate how to partition a rectangular region of length @math and height @math into @math rectangles of given areas @math using two-stage guillotine cuts, so as to minimize either (i) the sum of the perimeters, (ii) the largest perimeter, or (iii) the maximum aspect ratio of the rectangles. These problems play an important role in the ongoing Vietnamese land-allocation reform, as well as in the optimization of matrix multiplication algorithms. We show that the first problem can be solved to optimality in @math , while the two others are NP-hard. We propose mixed integer programming (MIP) formulations and a binary search-based approach for solving the NP-hard problems. Experimental analyses are conducted to compare the solution approaches in terms of computational efficiency and solution quality, for different objectives.
@cite_0: The present paper introduces and studies a new combinatorial clustering model for the consolidation of farmland. While the general problem turns out to be NP-hard even in quite restricted cases, the Size-restricted Minimum-k-Star Group Partition problem is solvable in polynomial time. Based on this tractability result, we derive a general approximation algorithm which, as the mathematical analysis and economic evaluation shows, performs well in theory and practice.
@cite_4: This paper examines the impact of farmland readjustment projects on farmland use and structural adjustment in Niigata, Japan. We use census data of rural communities for 1990 and 2000 to conduct pooled regression, first-difference, difference-in-differences, and propensity score matching estimations. We find positive impact of farmland readjustment projects in alleviating farmland abandonment and in facilitating outsourcing of agricultural works and farmland rental. The results suggest that farmland consolidation may be an effective option to resolve farmland fragmentation and to promote structural adjustment in concentrating farmland to efficient farmers which is a premise for strengthening the agricultural sector under economies of scale.
@cite_2: 
Other close variants of have been studied. @cite_0 @cite_4 considered the problem of decomposing a square or a rectangle into a number of rectangles of equal area so as to minimize the maximum rectangle perimeter. VLSI floorplan design and facility location applications also led to a number of related studies . @cite_2 proposed a local search and mathematical programming algorithm to solve rectangular packing problems where the shapes of the rectangles are adjustable within given perimeter and area constraints.