Any parallel program has abstractions that are shared by the program's multiple processes. Such shared abstractions can considerably affect the performance of parallel programs, on both distributed and shared memory multiprocessors. As a result, their implementation must be efficient, and such efficiency should be achieved without unduly compromising program portability and maintainability. The primary contribution of the DSA library is its representation of shared abstractions as objects that may be internally distributed across different nodes of a parallel machine. Such distributed shared abstractions (DSA) are encapsulated so that their implementations are easily changed while maintaining program portability across parallel architectures. The principal results presented are: a demonstration that the fragmentation of object state across different nodes of a multiprocessor machine can significantly improve program performance; and that such object fragmentation can be achieved without compromising portability by changing object interfaces. These results are demonstrated using implementations of the DSA library on several medium scale multiprocessors, including the BBN Butterfly, Kendall Square Research, and SGI shared memory multiprocessors. The DSA library's evaluation uses synthetic workloads and a parallel implementation of a branch and bound algorithm for solving the traveling salesperson problem (TSP).