On the complexity of planning for agent teams and its implications for single agent planning
If the complexity of planning for a single agent is described by some function f of the input, how much more difficult is it to plan for a team of n cooperating agents? If these agents are completely independent, we can simply solve n single agent problems, scaling linearly with the number of agents. But if all the agents interact tightly, we really need to solve a single problem that is n times larger, which could be exponentially (in n) harder to solve. Is a more general characterization possible? To formulate this question precisely, we minimally extend the standard STRIPS model to describe multi-agent planning problems. Then, we identify two problem parameters that help us answer our question. The first parameter is independent of the precise task the multi-agent system should plan for, and it captures the structure of the possible direct interactions between the agents via the tree-width of a graph induced by the team. The second parameter is task-dependent, and it captures the minimal number of interactions by the "most interacting" agent in the team that is needed to solve the problem. We show that multi-agent planning problems can be solved in time exponential only in these parameters. Thus, when these parameters are bounded, the complexity scales only polynomially in the size of the agent team. These results also have direct implications for the single-agent case: by casting single-agent planning tasks as multi-agent planning tasks, we can devise novel methods for decomposition-based planning for single agents. We analyze one such method, and use the techniques developed to provide some of the strongest tractability results for classical single-agent planning to date. (C) 2012 Elsevier B.V. All rights reserved.
complexity multi-agent planning tree-width classical planning