An approximation algorithm for scheduling on three dedicated machines

Approximation Schemes for Scheduling on Parallel Machines

We discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The goal is to optimize objective functions that solely depend on the machine completion times. As a main result, we identify some conditions on the objective function, under which the resulting scheduling problems possess a polynomial time approximation scheme. Our result cont...

A Faster Combinatorial Approximation Algorithm for Scheduling Unrelated Parallel Machines

We consider the problem of scheduling n independent jobs on m unrelated parallel machines without preemption. Job i takes processing time pi j on machine j , and the total time used by a machine is the sum of the processing times for the jobs assigned to it. The objective is to minimize makespan. The best known approximation algorithms for this problem compute an optimum fractional solution and...

Fast Monotone 3-Approximation Algorithm for Scheduling Related Machines

We consider the problem of scheduling n jobs to m machines of different speeds s.t. the makespan is minimized (Q||Cmax). We provide a fast and simple, deterministic monotone 3-approximation algorithm for Q||Cmax. Monotonicity is relevant in the context of truthful mechanisms: when each machine speed is only known to the machine itself, we need to motivate that machines declare their true speeds...

An approximation algorithm for scheduling two parallel machines with capacity constraints

We consider the problem of scheduling n independent jobs on two identical parallel machines, with a limit on the number of jobs that can be assigned to each single machine, so as to minimize the total weighted completion time of the jobs. We study a semide3nite programming-based approximation algorithm for solving this problem and prove that the algorithm has a worst case ratio at most 1.1626. ...

An Approximation Algorithm for the Two-Parallel Machines Scheduling Problem with Capacity Constraints