The dynamic version of the maximum flow problem allows the graph underlying the flow network to change over time. The graph receives corrections to its structure or capacities and consequently the value of the maximum flow is modified. These corrections arrive in real time. In this paper, parallel and sequential solutions to the real-time maximum flow problem are developed on the Reconfigurable Multiple Bus Machine (RMBM) model and on the Random Access Machine (RAM) model, respectively. The parallel solution successfully meets the deadlines imposed in real time, while the sequential one fails to do so. The two solutions are then applied to a real-time process scheduler, an extension of Stone's static twoprocessor allocation problem. The scheduler allows processes to be created and destroyed, the amount of communication between two processes to change with time, and so on. The parallel algorithm is always able to compute the optimal schedule, while the solution obtained sequentially is only an approximation. The improvement provided by the parallel approach over the sequential one is superlinear in the number of processors used by the parallel model. Key words and phrases: maximum flow, parallelism, real-time computation, module allocation. 1

A general framework is proposed for the study of real-time algorithms. The framework unifies previous algorithmic definitions of real-time computation. In it, state space traversal is used as a model for computational problems in a real-time environment. The proposed framework also employs a paradigm, known as discrete steepest descent, for algorithms designed to solve these problems. Sequential and parallel algorithms for traversing a state space by discrete steepest descent are then analyzed and compared. The analysis measures the value (or worth) of a computed solution. The quantity used in the evaluation may be the time required by an algorithm to reach the solution, the quality of the solution obtained, or any similar measure. The value of a real-time solution obtained in parallel is shown to be consistently superior to that of a solution computed sequentially by an amount superlinear in the size of the problem.

The nearest-neighbor method can successfully be applied to correct possible errors induced into bit strings transmitted over noisy communication channels or to classify samples into a predefined set of categories. These two applications are investigated under real-time constraints, when the deadlines imposed can dramatically alter the quality of the solution unless a parallel model of computation (in these cases, a linear array of processors) is used. We also study a class of real-time computations, referred to as reactive real-time systems, that are particularly sensitive to the first time constraint imposed. 1

COMPUTER \Lambda

A new computational paradigm is described which offers the possibility of superlinear (and sometimes unbounded) speedup, when parallel computation is used. The computations involved are subject only to given mathematical constraints and hence do not depend on external circumstances to achieve superlinear performance. The focus here is on geometric transformations. Given a geometric object A with some property, it is required to transform A into another object B which enjoys the same property. If the transformation requires several steps, each resulting in an intermediate object, then each of these intermediate objects must also obey the same property. We show that in transforming one triangulation of a polygon into another, a parallel algorithm achieves a superlinear speedup. In the case where a convex decomposition of a set of points is to be transformed, the improvement in performance is unbounded, meaning that a parallel algorithm succeeds in solving the problem as posed, while all sequential algorithms fail.