When deciding where to place access points in a wireless network, it is useful to model the signal propagation loss between a proposed antenna location and the areas it may cover. The indoor dominant path (IDP) model, introduced by Wölfle et al., is shown in the literature to have good validation and generalization error, is faster to compute than competing methods, and is used in commercial software such as WinProp, iBwave Design, and CellTrace. Previously, the algorithms known for computing it involved a worst-case exponential-time tree search, with pruning heuristics to speed it up. We prove that the IDP model can be reduced to a parametric shortest path computation on a graph derived from the walls in the floorplan. It therefore admits a quasipolynomial-time (i.e., $n^{O(\log n)}$) algorithm. We also give a practical approximation algorithm based on running a small constant number of shortest path computations. Its provable worst-case additive error (in dB) can be made arbitrarily small via appropriate choices of parameters, and is well below 1dB for reasonable choices. We evaluate our approximation algorithm empirically against the exact IDP model, and show that it consistently beats its theoretical worst-case bounds, solving the model exactly (i.e., no error) in the vast majority of cases.