In addition to partitioning data structures in the forward direction, from the global index to the local index, the programmer needs to recombine data structures in the reverse direction, from the local index back to the global index. The partition operators defined in Chapter 3 provided a recipe in the forward direction. Reverse partition operators defined in this chapter provide a recipe in the reverse direction. Almost all operations on data structures found in parallel applications are based on some mixture of forward and reverse partition operations.