3,227 research outputs found
Preemptive Scheduling of Equal-Length Jobs to Maximize Weighted Throughput
We study the problem of computing a preemptive schedule of equal-length jobs
with given release times, deadlines and weights. Our goal is to maximize the
weighted throughput, which is the total weight of completed jobs. In Graham's
notation this problem is described as (1 | r_j;p_j=p;pmtn | sum w_j U_j). We
provide an O(n^4)-time algorithm for this problem, improving the previous bound
of O(n^{10}) by Baptiste.Comment: gained one author and lost one degree in the complexit
Task Scheduling in Networks
Scheduling a set of tasks on a set of machines so as to yield an efficient schedule is a basic problem in computer science and operations research. Most of the research on this problem incorporates the potentially unrealistic assumption that communication between the different machines is instantaneous. In this paper we remove this assumption and study the problem of network scheduling, where each job originates at some node of a network, and in order to be processed at another node must take the time to travel through the network to that node.
Our main contribution is to give approximation algorithms and hardness proofs for fully general forms of the fundamental problems in network scheduling. We consider two basic scheduling objectives: minimizing the makespan and minimizing the average completion time. For the makespan, we prove small constant factor hardness-to-approximate and approximation results. For the average completion time, we give a log-squared approximation algorithm for the most general form of the problem. The techniques used in this approximation are fairly general and have several other applications. For example, we give the first nontrivial approximation algorithm to minimize the average weighted completion time of a set of jobs on related or unrelated machines, with or without a network
Matroid Coflow Scheduling
We consider the matroid coflow scheduling problem, where each job is comprised of a set of flows and the family of sets that can be scheduled at any time form a matroid. Our main result is a polynomial-time algorithm that yields a 2-approximation for the objective of minimizing the weighted completion time. This result is tight assuming P != NP. As a by-product we also obtain the first (2+epsilon)-approximation algorithm for the preemptive concurrent open shop scheduling problem
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Single machine scheduling with a generalized job-dependent cumulative effect
We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time
Energy Efficient Scheduling and Routing via Randomized Rounding
We propose a unifying framework based on configuration linear programs and
randomized rounding, for different energy optimization problems in the dynamic
speed-scaling setting. We apply our framework to various scheduling and routing
problems in heterogeneous computing and networking environments. We first
consider the energy minimization problem of scheduling a set of jobs on a set
of parallel speed scalable processors in a fully heterogeneous setting. For
both the preemptive-non-migratory and the preemptive-migratory variants, our
approach allows us to obtain solutions of almost the same quality as for the
homogeneous environment. By exploiting the result for the
preemptive-non-migratory variant, we are able to improve the best known
approximation ratio for the single processor non-preemptive problem.
Furthermore, we show that our approach allows to obtain a constant-factor
approximation algorithm for the power-aware preemptive job shop scheduling
problem. Finally, we consider the min-power routing problem where we are given
a network modeled by an undirected graph and a set of uniform demands that have
to be routed on integral routes from their sources to their destinations so
that the energy consumption is minimized. We improve the best known
approximation ratio for this problem.Comment: 27 page
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