842 research outputs found
How the structure of precedence constraints may change the complexity class of scheduling problems
This survey aims at demonstrating that the structure of precedence
constraints plays a tremendous role on the complexity of scheduling problems.
Indeed many problems can be NP-hard when considering general precedence
constraints, while they become polynomially solvable for particular precedence
constraints. We also show that there still are many very exciting challenges in
this research area
Throughput Maximization in Multiprocessor Speed-Scaling
We are given a set of jobs that have to be executed on a set of
speed-scalable machines that can vary their speeds dynamically using the energy
model introduced in [Yao et al., FOCS'95]. Every job is characterized by
its release date , its deadline , its processing volume if
is executed on machine and its weight . We are also given a budget
of energy and our objective is to maximize the weighted throughput, i.e.
the total weight of jobs that are completed between their respective release
dates and deadlines. We propose a polynomial-time approximation algorithm where
the preemption of the jobs is allowed but not their migration. Our algorithm
uses a primal-dual approach on a linearized version of a convex program with
linear constraints. Furthermore, we present two optimal algorithms for the
non-preemptive case where the number of machines is bounded by a fixed
constant. More specifically, we consider: {\em (a)} the case of identical
processing volumes, i.e. for every and , for which we
present a polynomial-time algorithm for the unweighted version, which becomes a
pseudopolynomial-time algorithm for the weighted throughput version, and {\em
(b)} the case of agreeable instances, i.e. for which if and only
if , for which we present a pseudopolynomial-time algorithm. Both
algorithms are based on a discretization of the problem and the use of dynamic
programming
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
Single-machine scheduling with stepwise tardiness costs and release times
We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems
A common framework and taxonomy for multicriteria scheduling problems with Interfering and competing Jobs: Multi-agent scheduling problems
Most classical scheduling research assumes that the objectives sought are common to all jobs to be
scheduled. However, many real-life applications can be modeled by considering different sets of jobs,
each one with its own objective(s), and an increasing number of papers addressing these problems has
appeared over the last few years. Since so far the area lacks a uni ed view, the studied problems
have received different names (such as interfering jobs, multi-agent scheduling, mixed-criteria, etc), some
authors do not seem to be aware of important contributions in related problems, and solution procedures
are often developed without taking into account existing ones. Therefore, the topic is in need of a common
framework that allows for a systematic recollection of existing contributions, as well as a clear de nition
of the main research avenues. In this paper we review multicriteria scheduling problems involving two or
more sets of jobs and propose an uni ed framework providing a common de nition, name and notation
for these problems. Moreover, we systematically review and classify the existing contributions in terms
of the complexity of the problems and the proposed solution procedures, discuss the main advances, and
point out future research lines in the topic
The Lazy Bureaucrat Scheduling Problem
We introduce a new class of scheduling problems in which the optimization is
performed by the worker (single ``machine'') who performs the tasks. A typical
worker's objective is to minimize the amount of work he does (he is ``lazy''),
or more generally, to schedule as inefficiently (in some sense) as possible.
The worker is subject to the constraint that he must be busy when there is work
that he can do; we make this notion precise both in the preemptive and
nonpreemptive settings. The resulting class of ``perverse'' scheduling
problems, which we denote ``Lazy Bureaucrat Problems,'' gives rise to a rich
set of new questions that explore the distinction between maximization and
minimization in computing optimal schedules.Comment: 19 pages, 2 figures, Latex. To appear, Information and Computatio
Throughput Maximization in the Speed-Scaling Setting
We are given a set of jobs and a single processor that can vary its speed
dynamically. Each job is characterized by its processing requirement
(work) , its release date and its deadline . We are also given
a budget of energy and we study the scheduling problem of maximizing the
throughput (i.e. the number of jobs which are completed on time). We propose a
dynamic programming algorithm that solves the preemptive case of the problem,
i.e. when the execution of the jobs may be interrupted and resumed later, in
pseudo-polynomial time. Our algorithm can be adapted for solving the weighted
version of the problem where every job is associated with a weight and
the objective is the maximization of the sum of the weights of the jobs that
are completed on time. Moreover, we provide a strongly polynomial time
algorithm to solve the non-preemptive unweighed case when the jobs have the
same processing requirements. For the weighted case, our algorithm can be
adapted for solving the non-preemptive version of the problem in
pseudo-polynomial time.Comment: submitted to SODA 201
Structural Properties of an Open Problem in Preemptive Scheduling
Structural properties of optimal preemptive schedules have been studied in a
number of recent papers with a primary focus on two structural parameters: the
minimum number of preemptions necessary, and a tight lower bound on `shifts',
i.e., the sizes of intervals bounded by the times created by preemptions, job
starts, or completions. So far only rough bounds for these parameters have been
derived for specific problems. This paper sharpens the bounds on these
structural parameters for a well-known open problem in the theory of preemptive
scheduling: Instances consist of in-trees of unit-execution-time jobs with
release dates, and the objective is to minimize the total completion time on
two processors. This is among the current, tantalizing `threshold' problems of
scheduling theory: Our literature survey reveals that any significant
generalization leads to an NP-hard problem, but that any significant
simplification leads to tractable problem.
For the above problem, we show that the number of preemptions necessary for
optimality need not exceed ; that the number must be of order
for some instances; and that the minimum shift need not be
less than . These bounds are obtained by combinatorial analysis of
optimal schedules rather than by the analysis of polytope corners for
linear-program formulations, an approach to be found in earlier papers. The
bounds immediately follow from a fundamental structural property called
`normality', by which minimal shifts of a job are exponentially decreasing
functions. In particular, the first interval between a preempted job's start
and its preemption is a multiple of 1/2, the second such interval is a multiple
of 1/4, and in general, the -th preemption occurs at a multiple of .
We expect the new structural properties to play a prominent role in finally
settling a vexing, still-open question of complexity
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