Geometric versions of the three-dimensional assignment problem under general norms

We discuss the computational complexity of special cases of the three-dimensional (axial) assignment problem where the elements are points in a Cartesian space and where the cost coefficients are the perimeters of the corresponding triangles measured according to a certain norm. (All our results also carry over to the corresponding special cases of the three-dimensional matching problem.) The minimization version is NP-hard for every norm, even if the underlying Cartesian space is 2-dimensional. The maximization version is polynomially solvable, if the dimension of the Cartesian space is fixed and if the considered norm has a polyhedral unit ball. If the dimension of the Cartesian space is part of the input, the maximization version is NP-hard for every Lp norm; in particular the problem is NP-hard for the Manhattan norm L1 and the Maximum norm L8 which both have polyhedral unit balls. Keywords: Combinatorial optimization; Computational complexity; 3-dimensional assignment problem; 3-dimensional matching problem; Polyhedral nor

Integrating Photosynthesis, Respiration, Biomass Partitioning, and Plant Growth: Developing a Microsoft Excel®-based Simulation Model of Wisconsin Fast Plant (

This paper demonstrates the development of a simple model of carbon flow during plant growth. The model was developed by six undergraduate students and their instructor as a project in a plant ecophysiology course. The paper describes the structure of the model including the equations that were used to implement it in Excel®, the plant growth experiments that were conducted to obtain information for parameterizing and testing the model, model performance, student responses to the modeling project, and potential uses of the model by other students