Abstract: With the development of network-based computing, computational problem-solving tends to be cooperatively carried out by distributed services.On this ground, how many times of interaction must be involved is decisive for the problem-solving efficiency, which calls for research on interaction-related complexity of a problem.Hence, a computation model, named interaction product, is proposed to replace Turing machines with the universal computation model.Interaction product consists of some automata interacting by accessing their shared cells, and its universality helps to realize the low cost and high accessibility of grids. Interaction complexity is defined based on this model since it explicitly describes interaction, and it differs from other interaction-related complexity in that it emphasizes interaction and at the same time strongly restricts the computational capability of the individuals.As an interaction-centric measure of problem-solving efficiency, interaction complexity helps to optimize grid applications.The relationship between interaction complexity and the classic time complexity is also discussed.