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We consider the time-convex hull problem in the presence of two orthogonalhighways H. In this problem, the travelling speed on the highway is faster thanoff the highway, and the time-convex hull of a point set P is the closure of Pwith respect to the inclusion of shortest time-paths. In this paper, we providethe algorithm for constructing the time-convex hull with two orthogonalhighways. We reach the optimal result of O(n log n) time for arbitrary highwayspeed in the L1-metric. For the L2-metric with infinite highway speed, we hitthe goal of O(n log n) time as well.

Optimal Construction for Time-Convex Hull with Two Orthogonal Highways in the L1-metric