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We develop a new framework for spatially optimizing infrastructure for CO₂ capture and storage (CCS). CCS is a complex and challenging problem: domestically deploying CCS at a meaningful scale will require linking hundreds of coal-fired power plants with CO₂ sequestration reservoirs through a dedicated and extensive (many tens-of-thousands of miles) CO₂ pipeline network. We introduce a unique method for generating a candidate network from scratch, from which the optimization model selects the optimal set of arcs to form the pipeline network. This new generation method can be applied to any network optimization problem including transmission line, roads, and telecommunication applications. We demonstrate the model and candidate network methodology using a real example of capturing CO₂ from coal-fired power plants in the US Midwest and storing the CO₂ in depleted oil and gas fields. Results …