Distributed integer programming
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In this thesis, we study distributed integer programming problems that involve multiple players with integer programming problems linked together with a common resource constraint. Our goal is to design decentralized algorithms that do not require a central processor to allocate the resource across the players to solve the overall problem. The algorithms that we design have optimality guarantees when applied to problems for which the marginal value of each additional resource is non-increasing. For problems that do not have this step-wise concave structure, we propose approximation algorithms and provide error bounds. We also perform experiments to evaluate the algorithms' average performance on problems without the desired structure. Finally, we consider the same problem in an online setting. We show that there exists no deterministic online algorithms for our problem that has the state of the art error bound. Therefore we propose a randomized decentralized online algorithm for our problem whose error bound matches the results in the literature.