Performance of Garey–Johnson algorithm for pipelined typed tasks systems

We consider a finite set of unit time execution tasks with release dates, due dates and precedence delays. The machines are partitionned into k classes. Each task requires one machine from a fixed class to be executed. The problem is the existence of a feasible schedule. This general problem is known to be N P-complete; many studies were devoted to the determination of polynomial time algorithms for some special subcasses, most of them based on a particular list schedule. The Garey-Johnson and Leung-Palem-Pnueli algorithms (respectively GJ and LPP in short) are both improving the due dates to build a priority list. They are modifiying them using necessary conditions until a fix point is reached. The present paper shows that these two algorithms are different implementations of a same generic one. The main consequence is that all the results valid for GJ algorithm, are also for LPP and vice versa. Keywords list scheduling algorithms • polynomial sub-problems • approximation algorithms 1 Introduction Scheduling problems with release and due dates have been considered for a long time, either in their decision version (is there a schedule meeting all the constraints ?) or in their optimization version, by minimizing the maximum lateness L max. Most of the decision problems are N P-complete once precedence and resource constraints are considered [6,12,15]. However, some particular instances have led to polynomial algorithms. Garey and Johnson [5] solved polynomially P 2|prec, p i = 1, r i , d i |L max and its preemptive version P 2|prec, pmtn, r i , d i |L max by using a particular list scheduling algorithm. This algorithm was extended to get approximation algorithms for the L max criteria with various hypothesis: parallel processors [8], preemptive jobs [7], communication delays [7], typed tasks systems, and unitary resource constraints scheduling problems [1].

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“…In the same way, Theorem 4 was proved by Benabid and Hanen [1] using initially GJ algorithm and is thus also valid for LPP algorithm:…”

Section: Approximation Algorithms Based On Gj Consistencysupporting

confidence: 53%

“…GJ consistency was introduced in [5] for solving polynomially the decision problem 2|prec, r i , d i , p i = 1|⋆. It was extended to typed-tasks systems in [1]. A wider extension is presented here to integrate precedence delays.…”

Section: Gj Consistencymentioning

confidence: 99%