Abstract

Abstract. Given a set 3- = {T1, T2, , T,} of tasks, each T/having execution time 1, an integer start-time si->0 and adeadlinedi> 0, alongwithprecedence constraintsamongthe tasks,weexamine the problem of determining whether there exists a schedule on two identical processors that executes each task in the time intervalbetween its start-timeand deadline.We present an O(n3) algorithm that constructs such a schedule whenever one exists. The algorithm may also be used in a binary search mode to find the shortest such schedule or to find a schedule that minimizesmaximum "tardiness".A number of natural extensions of this problem are seen to be NP-complete and hence probably intractable. Key words, multiprocessing systems, scheduling algorithms, NP-complete problems 1. Introduction. Since publication of the book Theory ofScheduling [4] by Conway, Maxwell, andMiller in 1967, considerableprogresshasbeenmade inthe mathematical analysis of abstract multiprocessing systems. One combinatorial model which is central to much of this work consists of a numberm of identical, independent processors, a finite set- {T1, T2, Tn} of tasks to be executed,

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