Symmetric multiprocessors (SMPs) dominate the high-end server market and are currently the primary candidate for constructing large scale multiprocessor systems. Yet, the design of efficient parallel algorithms for this platform currently poses several challenges. In this paper, we present a computational model for designing efficient algorithms for symmetric multiprocessors. We then use this model to create efficient solutions to two widely different types of problems - linked list prefix computations and generalized sorting. Our novel algorithm for prefix computations builds upon the sparse ruling set approach of Reid-Miller and Blelloch. Besides being somewhat simpler and requiring nearly half the number of memory accesses, we can bound our complexity with high probability instead of merely on average. Our algorithm for generalized sorting is a modification of our algorithm for sorting by regular sampling on distributed memory architectures. The algorithm is a stable sort which appears to be asymptotically faster than any of the published algorithms for SMPs. Both of our algorithms were implemented in C using POSIX threads and run on four symmetric multiprocessors - the IBM SP-2 (High Node), the HP-Convex Exemplar (S-Class), the DEC AlphaServer, and the Silicon Graphics Power Challenge. We ran our code for each algorithm using a variety of benchmarks which we identified to examine the dependence of our algorithm on memory access patterns. In spite of the fact that the processors must compete for access to main memory, both algorithms still yielded scalable performance up to 16 processors, which was the largest platform available to us. For some problems, our prefix computation algorithm actually matched or exceeded the performance of the standard sequential solution using only a single thread. Similarly, our generalized sorting algorithm always beat the performance of sequential merge sort by at least an order of magnitude, even with a single thread.