A Graph Theoretic Approach To Food Combination Problems
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Graph theory provides a useful representation of, and mathematical toolkit for, analyzing how things are connected together. This collection of research investigates the use of graph theory as a representation of how foods are connected together. The first two studies validate the subject questioning procedure used to create a graph model out of responses and the final study introduces a new approach to using this methodology to optimize field ration menus for the United States Army. In the first study, we began by asking subjects whether or not pairs of ingredients would be appropriate to combine on a salad. Next, using graph theoretic methods, we predicted which combinations of 3-8 components should go together. Subjects were then asked whether or not particular combinations were appropriate to combine on a salad. A paired Wilcoxon test between the predicted and non-predicted combinations was significant for all combination sizes. The second study tested the principle of supercombinatorality, i.e. that food combinations (of more than two items) that are fully compatible on a pairwise basis are more compatible than combinations that are not fully compatible pairwise. This study extended the previous findings to group data. Purchase intent responses to pairs of different pizza toppings were collected and used to predict pizzas (with one to 6 toppings) that would appeal to the entire group. Results showed purchase interest to be higher for the predicted pizzas than for non pre- dicted pizzas supporting the supercombinatorality principle. The final study extends the graph theory representation to military rations known as Meal-Ready-to-Eat or MREs. MRE menus are composed of 11 different food categories (entrĀ“ e, side, snack, etc.) and there are multiple items e available in each category. From these items there are over 22 billion potential menus. Categories and items were screened to create a list of the most important ones and we asked soldiers whether or not pairwise combinations of components were appropriate to combine in a meal. Using graph theoretic tools, predictions were made of optimal MRE menus and rankings were attached to prediction in order to assist the product developers in screening old and new menu concepts.
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Halpern, Bruce Peter
Acree, Terry Edward