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. |