Parameterized Analysis of Assignment Under Multiple Preferences
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The Assignment problem is a fundamental, well-studied problem in the intersection of Social Choice, Computational Economics and Discrete Allocation. In the Assignment problem, we seek a pareto optimal allocation of items to agents given the preferences of the agents. We introduce a generalized version of this problem, where each agent is equipped with multiple incomplete preference lists: each list (called a layer) is a ranking of items in a possibly different way according to a different criterion. We introduce a new concept of pareto optimality, and study the generalized version of the problem from the perspective of Parameterized Complexity. Here, we consider several natural parameters such as the number of layers, number of agents, number of items, and maximal length of a preference list; we present a comprehensive picture of the parameterized complexity of the problem with respect to these parameters.
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