Discrete Steepest Descent in Real Time

Abstract

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.