The authors present exact characterizations of structures on which the greedy algorithm produces optimal solutions. Our characterization, which are called matroid embeddings, complete the partial characterizations of Rado [A note on independent functions, Proc. London Math. Soc., 7 (1957), pp. 300–320], Gale [Optimal assignments in an ordered set, J. Combin. Theory, 4 (1968), pp. 176–180], and Edmonds [Matroids and the greedy algorithm, Math. Programming, 1 (1971), pp. 127–136], (matroids), and of Korte and Lovasz [Greedoids and linear object functions, SIAM J. Alg. Discrete Meth., 5 (1984), pp. 239–248] and [Mathematical structures underlying greedy algorithms, in Fundamentals of Computational Theory, LNCS 177, Springer-Verlag, 1981, pp. 205–209] (greedoids). It is shown that the greedy algorithm optimizes all linear objective functions if and only if the problem structure (phrased in terms of either accessible set systems or hereditary languages) is a matroid embedding. An exact characterization of the objective functions optimized by the greedy algorithm on matroid embeddings is also presented. Finally, the authors present an exact characterization of the structures on which the greedy algorithm optimizes all bottleneck functions, structures that are less constrained than matroid embeddings.

Adaptive quadrature methods are usually characterized as either local or global.The methods are distinguished by the scope and nature of the information used to determine when algorithm termination should occur and which intervals should be selected for refinement.By treating quadrature as the generation and search of a tree whose nodes represent intervals, a unified nonalgorithmi¢ framework is developed which encompasses both approaches.This framework provides a method for improving the numerical properties of local adaptive quadrature with respect to termination of intervals by relative error criteria, and total algorithm termination due to excessive function evaluations.The framework also suggests heuristics for interval selection in global adaptive quadrature that bring the actual error closer to the requested tolerance.Extensive computational experience with several heuristics for global adaptive quadrature is described Categories and Subject Descriptors: G.

The effective utilization of single-instruction-multiple-data stream machines depends heavily on being able to arrange the data elements of arrays in parallel memory modules so that memory conflicts are avoided when the data are fetched. Several classes of storage algorithms are presented. Necessary and sufficient conditions are derived which can be used to determine if all conflict can be avoided. For the matrix subparts most often demanded in numerical analysis computations, whenever the class of storage algorithms called periodic skewing schemes provides conflict-free access, the subclass called linear skewing schemes also provides such access.