Antenna problem is a phenomenon of plasma induced gate oxide degradation. It directly affects manufacturability of VLSI circuits, especially in deep-submicron technology using high density plasma. Diode insertion is a very effective way to solve this problem. Ideally diodes are inserted directly under the wires that violate antenna rules. But in today's high-density VLSI layouts, there is simply not enough room for iounder-the-wirel. diode insertion for all wires. Thus it is necessary to insert many diodes at legal ieoff-wirel- locations and extend the antenna-rule violating wires to connect to their respective diodes. Previously only simple heuristic algorithms were available for this diode insertion and routing problem. In this paper, we show that the diode insertion and routing problem for an arbitrary given number of routing layers can be optimally solved in polynomial time. Our algorithm guarantees to find a feasible diode insertion and routing solution whenever one exists. Moreover, we can guarantee to find a feasible solution to minimize a cost function of the form \alpha \cdot L + \beta \cdot N where \cdot L is the total length of extension wires and \cdot N is the total number of vias on the extension wires. Experimental results show that our algorithm is very efficient.