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We push the limit in planning collision-free motions for routing uniformlabeled discs in two dimensions. First, from a theoretical perspective, we showthat the constant-factor time-optimal routing of labeled discs can be achievedusing a polynomial-time algorithm with robot density over $50\%$ in the limit(i.e., over half of the workspace may be occupied by the discs). Second, from amore practical standpoint, we provide a high performance algorithm thatcomputes near-optimal (e.g., $1.x$) solutions under the same density setting.

Coordinating the Motion of Labeled Discs with Optimality Guarantees under Extreme Density