
Scheduling on (Un)Related Machines with Setup Times
We consider a natural generalization of scheduling n jobs on m parallel ...
read it

Complexity of Scheduling Few Types of Jobs on Related and Unrelated Machines
The task of scheduling jobs to machines while minimizing the total makes...
read it

SpeedRobust Scheduling
The speedrobust scheduling problem is a twostage problem where given m...
read it

Scheduling to Approximate Minimization Objectives on Identical Machines
This paper considers scheduling on identical machines. The scheduling ob...
read it

Geometry of Scheduling on Multiple Machines
We consider the following general scheduling problem: there are m identi...
read it

Faulttolerant parallel scheduling of arbitrary length jobs on a shared channel
We study the problem of scheduling jobs on faultprone machines communic...
read it

An Intrinsically Universal Family of Signal Machines
Signal machines form an abstract and perfect model of collision computin...
read it
Malleable scheduling beyond identical machines
In malleable job scheduling, jobs can be executed simultaneously on multiple machines with the processing time depending on the number of allocated machines. Jobs are required to be executed nonpreemptively and in unison, in the sense that they occupy, during their execution, the same time interval over all the machines of the allocated set. In this work, we study generalizations of malleable job scheduling inspired by standard scheduling on unrelated machines. Specifically, we introduce a general model of malleable job scheduling, where each machine has a (possibly different) speed for each job, and the processing time of a job j on a set of allocated machines S depends on the total speed of S for j. For machines with unrelated speeds, we show that the optimal makespan cannot be approximated within a factor less than e/e1, unless P = NP. On the positive side, we present polynomialtime algorithms with approximation ratios 2e/e1 for machines with unrelated speeds, 3 for machines with uniform speeds, and 7/3 for restricted assignments on identical machines. Our algorithms are based on deterministic LP rounding and result in sparse schedules, in the sense that each machine shares at most one job with other machines. We also prove lower bounds on the integrality gap of 1+φ for unrelated speeds (φ is the golden ratio) and 2 for uniform speeds and restricted assignments. To indicate the generality of our approach, we show that it also yields constant factor approximation algorithms (i) for minimizing the sum of weighted completion times; and (ii) a variant where we determine the effective speed of a set of allocated machines based on the L_p norm of their speeds.
READ FULL TEXT
Comments
There are no comments yet.