You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: In this paper we deal with two geometric problems arising from heterogeneous parallel computing: how to partition the unit square into p rectangles of given area s 1 , s 2 , . . . ,s p (such that Σ i=1 p s i = 1 ), so as to minimize either (i) the sum of the p perimeters of the rectangles or (ii) the largest perimeter of the p rectangles? For both problems, we prove NP-completeness and we introduce a 7 4 -approximation algorithm for (i) and a @math -approximation algorithm for (ii).
Finally, [1] considered and as a building block to design approximation algorithms for and when the general rectangular region is a square. The authors introduced an exact @math algorithm for and two approximation algorithms for . The complexity status of remained open. Moreover, has not been studied to this date. These methodological gaps along with the relevance of these problems for the Vietnamese land reform are a strong motivation for additional research.