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

Scheduling Bidirectional Traffic on a Path

We study the fundamental problem of scheduling bidirectional traffic along a path composed of multiple segments. The main feature of the problem is that jobs traveling in the same direction can be scheduled in quick succession on a segment, while jobs in opposing directions cannot cross a segment at the same time. We show that this tradeoff makes the problem significantly harder than the related flow shop problem, by proving that it is NP-hard even for identical jobs. We complement this result with a PTAS for a single segment and non-identical jobs. If we allow some pairs of jobs traveling in different directions to cross a segment concurrently, the problem becomes APX-hard even on a single segment and with identical jobs. We give polynomial algorithms for the setting with restricted compatibilities between jobs on a single and any constant number of segments, respectively

Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model

We consider online scheduling on multiple machines for jobs arriving one-by-one with the objective of minimizing the makespan. For any number of identical parallel or uniformly related machines, we provide a competitive-ratio approximation scheme that computes an online algorithm whose competitive ratio is arbitrarily close to the best possible competitive ratio. We also determine this value up to any desired accuracy. This is the first application of competitive-ratio approximation schemes in the online-list model. The result proves the applicability of the concept in different online models. We expect that it fosters further research on other online problems

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

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 $O(\log n/\log \log n)$-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here $n$ 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

Complexity of scheduling multiprocessor tasks with prespecified processor allocations

We investigate the computational complexity of scheduling multiprocessor tasks with prespecified processor allocations. We consider two criteria: minimizing schedule length and minimizing the sum of the task completion times. In addition, we investigate the complexity of problems when precedence constraints or release dates are involved

Order Acceptance and Scheduling: A Taxonomy and Review

Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area

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;