reconstructed exactly by patching together in some appropriate way the pieces computed in the cells. These pieces can be calculated in parallel in each cell, hence the name trajectory parallelization. The method in Ref.  is restricted to equilibrium systems and exploits the time-reversibility of the dynamics. The method in Refs.  is more costly but it works also for nonequilibrium systems. To explain how the latter method works, we first recall how to construct the cells using the Voronoi tessellation associated with a given set of generating points or centers [@miles6; @fts]. Denoting these centers by $\zz_{\alpha}
\in \Omega \subset \RR^d$, with $\alpha=1,\ldots,\Lambda$, the Voronoi cell $B_\alpha$ associated to $\zz_{\alpha}$ contains all the points that are closer to $\zz_\alpha$ than to any other center, i.e. (see Fig. \[fig:voronoi\] for an illustration) $$\label{eq:Bk}
  B_{\alpha}= 
  \{\zz \in \Omega \; : \; 
  \|\zz - \zz_{\alpha}\|<\|\zz-\zz_{\beta}\| \; 
  \text{for all} \; \beta \ne \alpha  \},$$ where $\|\cdot\|$ is some appropriate norm (e.g. the Euclidean norm in which case $\|\zz\|^2=\sum_{i=1}^d z_i^2$).

![Representation of a portion of the Voronoi tessellation in two-dimension, where point $\zz_\alpha$ is the generator of cell $B_\alpha$ and point $\zz_\beta$ the generator of cell $B_\beta$. Pieces of restricted trajectory inside $B_\alpha$ are shown in 