Complexity of Computer Computations, Softcover reprint of the original 1st ed. 1972 Proceedings of a symposium on the Complexity of Computer Computations, held March 20–22, 1972, at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, and sponsored by the Office of Naval Research, Mathematics Program, IBM World Trade Co The IBM Research Symposia Series

The Symposium on the Complexity of Computer Compu­ tations was held at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York, March 20-22, 1972. These Proceedings contain all papers presented at the Symposium together with a transcript of the concluding panel discussion and a comprehensive bibliography of the field. The Symposium dealt with complexity studies closely re­ lated to how computations are actually performed on computers. Although this area of study has not yet found an appropriate or generally accepted name, the area is recognizable by the signif­ icant commonality in problems, approaches, and motivations. The area can be described and delineated by examples such as the following. (1) Determining lower bounds on the number of operations or steps required for computational solutions of specific problems such as matrix and polynomial calculations, sorting and other combinatorial problems, iterative com­ putations, solving equations, and computer resource allocation. (2) Developing improved algorithms for the solution of such problems which provide good upper bounds on the number of required operations, along with experimental and v vi PREFACE theoretical evidence concerning the efficiency and numer­ ical accuracy of those algorithms. (3) Studying the effects on the efficiency of computation brought about by variations in sequencing and the intro­ duction of parallelism.

Evaluation of Rational Functions.- Solving Linear Equations by Means of Scalar Products.- Simple Proofs of Lower Bounds for Polynomial Evaluation.- On Obtaining Upper Bounds on the Complexity of Matrix Multiplication.- Efficient Iterations for Algebraic Numbers.- Parallel Iteration Methods.- The Computational Complexity of Iterative Methods for Systems of Nonlinear Equations.- The Computational Complexity of Elliptic Partial Differential Equations.- Reducibility Among Combinatorial Problems.- Permuting Information in Idealized Two-Level Storage.- An n log n Algorithm to Distribute n Records Optimally in a Sequential Access File.- Toward a Lower Bound for Sorting Networks.- Isomorphism of Planar Graphs.- Efficiency of Equivalence Algorithms.- Panel Discussion.- Name Index.