2 research outputs found
Cardinality Constrained Scheduling in Online Models
Makespan minimization on parallel identical machines is a classical and
intensively studied problem in scheduling, and a classic example for online
algorithm analysis with Graham's famous list scheduling algorithm dating back
to the 1960s. In this problem, jobs arrive over a list and upon an arrival, the
algorithm needs to assign the job to a machine. The goal is to minimize the
makespan, that is, the maximum machine load. In this paper, we consider the
variant with an additional cardinality constraint: The algorithm may assign at
most jobs to each machine where is part of the input. While the offline
(strongly NP-hard) variant of cardinality constrained scheduling is well
understood and an EPTAS exists here, no non-trivial results are known for the
online variant. We fill this gap by making a comprehensive study of various
different online models. First, we show that there is a constant competitive
algorithm for the problem and further, present a lower bound of on the
competitive ratio of any online algorithm. Motivated by the lower bound, we
consider a semi-online variant where upon arrival of a job of size , we are
allowed to migrate jobs of total size at most a constant times . This
constant is called the migration factor of the algorithm. Algorithms with small
migration factors are a common approach to bridge the performance of online
algorithms and offline algorithms. One can obtain algorithms with a constant
migration factor by rounding the size of each incoming job and then applying an
ordinal algorithm to the resulting rounded instance. With this in mind, we also
consider the framework of ordinal algorithms and characterize the competitive
ratio that can be achieved using the aforementioned approaches.Comment: An extended abstract will appear in the proceedings of STACS'2