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Redundant via insertion is a good solution to reduce the yield loss by via failure. However, the existing methods are all post-layout optimizations that insert redundant via after detailed routing. In this paper, we propose the first routing algorithm that considers feasibility of redundant via insertion in the detailed routing stage. Our routing problem is formulated as maze routing with redundant via constraints. The problem is transformed to a multiple constraint shortest path problem, and solved by Lagrangian relaxation technique. Experimental results show that our algorithm can find routing layout with much higher rate of redundant via than conventional maze routing.