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As the technology node advances into the nanometer era, via-open defects are one of the dominant failures due to the copper cladding process. To improve via yield and reliability, redundant-via insertion is a highly recommended technique proposed by foundries. Traditionally, double-via insertion is performed at the postlayout stage. The increasing design complexity, however, leaves very limited space for postlayout optimization. It is thus desirable to consider the double-via insertion at both the routing and postrouting stages. In this paper, we present a new full-chip gridless routing system considering double-via insertion for yield enhancement. To fully consider double vias, the router applies a novel two-pass, bottom-up routability-driven routing framework and features a new redundant-via aware detailed maze routing algorithm (which could be applied to both gridless and grid-based routing). We also propose a graph-matching based post-layout double-via insertion algorithm to achieve a higher insertion rate. In particular, the algorithm is optimal for grid-based routing with up to three routing layers and the stacked-via structure. Experiments show that our methods significantly improve the via count, number of dead vias, double-via insertion rates, and running times.