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Travel Depth, introduced by Coleman and Sharp in 2006, is a physical interpretation of molecular depth, a term frequently used to describe the shape of a molecular active site or binding site. Travel Depth can be seen as the physical distance a solvent molecule would have to travel from a point of the surface, i.e., the Solvent-Excluded Surface (SES), to its convex hull. Existing algorithms providing an estimation of the Travel Depth are based on a regular sampling of the molecule volume and the use of the Dijkstra's shortest path algorithm. Since Travel Depth is only defined on the molecular surface, this volume-based approach is characterized by a large computational complexity due to the processing of unnecessary samples lying inside or outside the molecule. In this paper, we propose a surface-based approach that restricts the processing to data defined on the SES. This algorithm significantly reduces the complexity of Travel Depth estimation and makes possible the analysis of large macromolecule surface shape description with high resolution. Experimental results show that compared to existing methods, the proposed algorithm achieves accurate estimations with considerably reduced processing times.