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This paper presents a decentralized algorithm for the coordinated assembly of 3-D objects that consist of multiple types of parts, using a networked team of robots. We describe the algorithm and analyze its convergence and adaptation properties. We partition construction in two tasks: tool delivery and assembly. Each task is performed by a networked team of specialized robots. We analyze the performance of the algorithms using the balls into bins problem and show their adaptation to failure of robots, dynamic constraints, multiple types of elements, and reconfiguration. We instantiate the algorithm to building truss-like objects using rods and connectors. We implement the algorithm in simulation and show results to construct 2-D and 3-D parts. Finally, we describe hardware implementation of the algorithms, where mobile manipulators assemble smart parts with IR beacons.