1 research outputs found
Hierarchy-Based Algorithms for Minimizing Makespan under Precedence and Communication Constraints
We consider the classic problem of scheduling jobs with precedence
constraints on a set of identical machines to minimize the makespan objective
function. Understanding the exact approximability of the problem when the
number of machines is a constant is a well-known question in scheduling theory.
Indeed, an outstanding open problem from the classic book of Garey and Johnson
asks whether this problem is NP-hard even in the case of 3 machines and
unit-length jobs. In a recent breakthrough, Levey and Rothvoss gave a
-approximation algorithm, which runs in nearly quasi-polynomial
time, for the case when job have unit lengths. However, a substantially more
difficult case where jobs have arbitrary processing lengths has remained open.
We make progress on this more general problem. We show that there exists a
-approximation algorithm (with similar running time as that of
Levey and Rothvoss) for the non-migratory setting: when every job has to be
scheduled entirely on a single machine, but within a machine the job need not
be scheduled during consecutive time steps. Further, we also show that our
algorithmic framework generalizes to another classic scenario where, along with
the precedence constraints, the jobs also have communication delay constraints.
Both of these fundamental problems are highly relevant to the practice of
datacenter scheduling