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It is well known that the solution quality of the detailed routing phase is heavily influenced by the order in which nets are routed. To alleviate this situation a number of routing strategies have been developed that ripup and reroute (R&R) previously-routed nets that "block" the current net. In the R&R approach, there is not a significant amount of control over the solution quality (e.g., length, delay) for the ripped-up nets. We propose a detailed router ROAD (bump&Refit based Optimal Detailed router) that explores the solution space using an approach called bump-and-refit (B&R) in which the global routes of prior-routed nets are not changed but their track assignments are systematically altered in order to make space for the current net being routed. B&R thus does not have the above drawback of R&R. We start with an initial depth-first search method for this purpose that is optimal in finding a detailed routing solution with the minimum number of tracks irrespective of the net routing order. We then develop various optimality-preserving speedup methods including search space pruning based on clique detection and learning about and remembering unsuccessful search spaces, and second-level or lookahead transition costs. The combination of these methods results in an average speedup of 604 for small to medium VPR circuits and an extrapolated speedup of more than 5763 for larger circuits. Furthermore, comparison of ROAD run times to that of VPR's estimated detailed routing phase show that we are almost two times faster than VPR. This is noteworthy because an optimal detailed router is able to obtain solutions in reasonable times which are also faster than those of a nonoptimal (though effective) router.