Decentralized Assignment Reasoning Using Collaborative Local Mediation

The collaborative linear assignment problem (CLAP) is a recent framework being developed to provide an intellectual basis for investigating uncluttered agent-based solutions for a fundamental class of combinatorial assignment (or allocation) applications. One key motivation of the research on CLAP is the hope that it can shed new light on adopting agent approaches for solving traditional combinatorial problems in general. To accommodate the various levels of control on agent sociability, typically different application-specific solutions to CLAP are required. In this paper, we take an architectural perspective, classifying solutions according to three typical control structures, namely, centralized, distributed, and decentralized. Existing work focuses mainly on centralized and distributed systems. In this paper, based on the Multi-Agent Assignment Algorithm ({\rm MA}^{3}) used for distributed systems, we propose a new mechanism for a totally decentralized architecture. This proposed mechanism incorporates a novel idea called collaborative Local Mediation (LM), therefore, we term this mechanism {\rm MA}^{3}{\hbox{-}}{\rm{LM}}. We prove that the decentralized {\rm MA}^{3}{\hbox{-}}{\rm{LM}} does not increase the worst-case reasoning complexity when compared to its partially decentralized counterpart. An example illustrates the new mechanism, with emphasis on how it performs collaborative local mediation.