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Existing layout-optimization methods for both capacitive and inductive (RLC) crosstalk reduction assume a set of interconnects with a priori given crosstalk bounds in a routing region. RLC crosstalk budgeting is critical for effectively applying these methods at the full-chip level. In this paper, we formulate a full-chip routing optimization problem with RLC crosstalk budgeting, and solve this problem with a multiphase algorithm. In phase I, we solve an optimal RLC crosstalk budgeting based on linear programming to partition crosstalk bounds at sinks into bounds for net segments in routing regions. In phase II, we perform simultaneous shield insertion and net ordering to meet the partitioned crosstalk bounds in each region. In phase III, we carry out a local refinement procedure to reduce the total number of shields. Compared with the best alternative approach in experiments, the proposed algorithm reduces the total routing area by up to 5.71% and uses less runtime. To the best of our knowledge, this work is the first in-depth study on full-chip routing optimization with RLC crosstalk budgeting.