Variable influence duration (VID) join is a novel spatio-temporal join operation between a set T of trajectories and a set P of spatial points. Here, trajectories are traveling histories of moving objects (e.g., travelers), and spatial points are points of interest (POIs, e.g., restaurants). VID join rets all pairs of (τs, p) if τs is spatially close to p for a long period of time, where τs is a segment of trajectory τ ∈ T and p ∈ P. Each reted (τs, p) implies that the moving object associated with τs stayed at p (e.g., having dinner at a restaurant). Such information is useful in many aspects, such as targeted advertising, social security, and social activity analysis. The concepts of influence and influence duration are introduced to measure the spatial closeness between τ and p, and the time spanned, respectively. Compared to the conventional spatio-temporal join, the VID join is more challenging since the join condition varies for different POIs, and the additional temporal requirement cannot be indexed effectively. To process the VID join e?ciently, three algorithms are developed and several optimization techniques are applied, including spatial duplication reuse and time duration based pruning. The performance of the developed algorithms is verified by extensive experiments on real spatial data.