Moderately exponential approximation for makespan minimization on related machines
نویسندگان
چکیده
منابع مشابه
Eecient Approximation Algorithm for Minimizing Makespan on Uniformly Related Machines
We obtain a new eecient approximation algorithm for scheduling precedence constrained jobs on machines with diierent speeds. The setting is as follows. There are n jobs, job j requires p j units of processing. The jobs are to be scheduled on a set of m machines. Machine i has a speed s i ; it takes p j =s i units of time for machine i to process job j. The precedence constraints on the jobs are...
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We consider the problem of scheduling n jobs to minimize the makespan on m unrelated machines, where job j requires time pij if processed on machine i. A classic algorithm of Lenstra et al. [5] yields the best known approximation ratio of 2 for the problem. Improving this bound has been a prominent open problem for over two decades. In this paper we obtain a tighter bound for a wide subclass of...
متن کاملExact and Approximation Algorithms for Makespan Minimization on Unrelated Parallel Machines
The NP-hard problem addressed in this paper is well known in the scheduling literature as Rl( C,,,. We propose lower bounds based on Lagrangian relaxations and additive techniques. We then introduce new cuts which eliminate infeasible disjunctions on the cost function value, and prove that the bounds obtained through such cuts dominate the previous bounds. These results are used to obtain exact...
متن کاملLower bounds for online makespan minimization on a small number of related machines
Lukasz Jeż was partially supported by MNiSW grant N N206 368839, 2010–2013, a scholarship co-financed by an ESF project Human Capital, by the grant IAA100190902 of GA AV ČR, and by EUROGIGA project GraDR. Jarett Schwartz was partially supported by the National Science Foundation Graduate Research Fellowship and the Fulbright Fellowship. Jǐŕı Sgall was supported by the Center of Excellence – Ins...
متن کاملAn Eecient Approximation Algorithm for Minimizing Makespan on Uniformly Related Machines
We give a new eecient approximation algorithm for scheduling precedence constrained jobs on machines with diierent speeds. The setting is as follows. There are n jobs 1; : : : ; n where job j requires pj units of processing. The jobs are to be scheduled on a set of m machines. Machine i has a speed si; it takes pj=si units of time for machine i to process job j. The precedence constraints on th...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2013
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.03.020