#### Abstract

My research focuses on constructing and analyzing systems of intelligent, autonomous agents. These agents may include people, physical robots, or software programs acting as assistants, teammates, opponents, or trading partners. In a large class of multi-agent scenarios, the effect of local interactions between agents can be compactly represented as a network structure such as a distributed constraint optimization problem (DCOP) for cooperative domains. Collaboration between large groups of agents, given such a network, can be difficult to achieve; often agents can only manage to collaborate in smaller subgroups of a certain size, in order to find a workable solution in a timely manner. The goal of my thesis is to provide algorithms to enable networks of agents that are bounded in this way to quickly find high-quality solutions, as well as theoretical results to understand key properties of these solutions. Relevant domains for my work include personal assistant agents, sensor networks, and teams of autonomous robots. In particular, this thesis considers the case in which agents optimize a DCOP by forming groups of one or more agents until no group of k or fewer agents can possibly improve the solution; we define this type of local optimum, and any algorithm guaranteed to reach such a local optimum, as k-optimal. In this document, I present four key contributions related to k-optimality. The first set of results are worst-case guarantees on the solution quality of k-optima in a DCOP.