6,804 research outputs found
Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and
complexity research. A novel approach to machine scheduling problems are
fixed-parameter algorithms. To stimulate this thriving research direction, we
propose 15 open questions in this area whose resolution we expect to lead to
the discovery of new approaches and techniques both in scheduling and
parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc
Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments
In the current work we introduce a novel estimation of distribution algorithm
to tackle a hard combinatorial optimization problem, namely the single-machine
scheduling problem, with uncertain delivery times. The majority of the existing
research coping with optimization problems in uncertain environment aims at
finding a single sufficiently robust solution so that random noise and
unpredictable circumstances would have the least possible detrimental effect on
the quality of the solution. The measures of robustness are usually based on
various kinds of empirically designed averaging techniques. In contrast to the
previous work, our algorithm aims at finding a collection of robust schedules
that allow for a more informative decision making. The notion of robustness is
measured quantitatively in terms of the classical mathematical notion of a norm
on a vector space. We provide a theoretical insight into the relationship
between the properties of the probability distribution over the uncertain
delivery times and the robustness quality of the schedules produced by the
algorithm after a polynomial runtime in terms of approximation ratios
Asymptotically Optimal Approximation Algorithms for Coflow Scheduling
Many modern datacenter applications involve large-scale computations composed
of multiple data flows that need to be completed over a shared set of
distributed resources. Such a computation completes when all of its flows
complete. A useful abstraction for modeling such scenarios is a {\em coflow},
which is a collection of flows (e.g., tasks, packets, data transmissions) that
all share the same performance goal.
In this paper, we present the first approximation algorithms for scheduling
coflows over general network topologies with the objective of minimizing total
weighted completion time. We consider two different models for coflows based on
the nature of individual flows: circuits, and packets. We design
constant-factor polynomial-time approximation algorithms for scheduling
packet-based coflows with or without given flow paths, and circuit-based
coflows with given flow paths. Furthermore, we give an -approximation polynomial time algorithm for scheduling circuit-based
coflows where flow paths are not given (here is the number of network
edges).
We obtain our results by developing a general framework for coflow schedules,
based on interval-indexed linear programs, which may extend to other coflow
models and objective functions and may also yield improved approximation bounds
for specific network scenarios. We also present an experimental evaluation of
our approach for circuit-based coflows that show a performance improvement of
at least 22% on average over competing heuristics.Comment: Fixed minor typo
Clips: a capacity and lead time integrated procedure for scheduling.
We propose a general procedure to address real life job shop scheduling problems. The shop typically produces a variety of products, each with its own arrival stream, its own route through the shop and a given customer due date. The procedure first determines the manufacturing lot sizes for each product. The objective is to minimize the expected lead time and therefore we model the production environment as a queueing network. Given these lead times, release dates are set dynamically. This in turn creates a time window for every manufacturing order in which the various operations have to be sequenced. The sequencing logic is based on a Extended Shifting Bottleneck Procedure. These three major decisions are next incorporated into a four phase hierarchical operational implementation scheme. A small numerical example is used to illustrate the methodology. The final objective however is to develop a procedure that is useful for large, real life shops. We therefore report on a real life application.Model; Models; Applications; Product; Scheduling;
Scheduling under Linear Constraints
We introduce a parallel machine scheduling problem in which the processing
times of jobs are not given in advance but are determined by a system of linear
constraints. The objective is to minimize the makespan, i.e., the maximum job
completion time among all feasible choices. This novel problem is motivated by
various real-world application scenarios. We discuss the computational
complexity and algorithms for various settings of this problem. In particular,
we show that if there is only one machine with an arbitrary number of linear
constraints, or there is an arbitrary number of machines with no more than two
linear constraints, or both the number of machines and the number of linear
constraints are fixed constants, then the problem is polynomial-time solvable
via solving a series of linear programming problems. If both the number of
machines and the number of constraints are inputs of the problem instance, then
the problem is NP-Hard. We further propose several approximation algorithms for
the latter case.Comment: 21 page
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