The flip-chip package is introduced for modern integrated circuit (IC) designs with higher integration density and larger I/O counts. In this paper, we consider the pre-assignment flip-chip routing problem with predefined connections between driver pads and bump pads. This problem has been shown to be much more difficult than the free-assignment one, but is more popular in real-world designs because the connections between driver pads and bump pads are typically predetermined by IC or packaging designers. Based on the concept of routing sequence exchange, we propose a very efficient approach to guide the global routing by computing the longest common subsequence and the maximum planar subset of chords for pre-assignment flip-chips. We observe that the existing work over-constrains the capacity of a routing tile, which might miss some critical solution space with a better routing solution (e.g., smaller wirelength), and provide a remedy for this insufficiency to identify a better solution in a more complete solution space. We also develop a constant-time routability analyzer to check if a given set of wires can pass through a tile. Experimental results show that our router can achieve a 125× speedup with even better solution quality (same routability with slightly smaller wirelength), compared with a state-of-the-art flip-chip router based on integer linear programming.