TY - JOUR

T1 - On the complexity of planning for agent teams and its implications for single agent planning

AU - Brafman, Ronen I.

AU - Domshlak, Carmel

N1 - Funding Information:
The work was partly supported by the Israel Science Foundation (ISF) grant 1101/07.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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 treewidth 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 singleagent 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.

AB - 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 treewidth 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 singleagent 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.

KW - Classical planning

KW - Complexity

KW - Multi-agent planning

KW - Tree-width

UR - http://www.scopus.com/inward/record.url?scp=84893117233&partnerID=8YFLogxK

U2 - 10.1016/j.artint.2012.08.005

DO - 10.1016/j.artint.2012.08.005

M3 - Article

AN - SCOPUS:84893117233

VL - 198

SP - 52

EP - 71

JO - Artificial Intelligence

JF - Artificial Intelligence

SN - 0004-3702

ER -