15,147 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
The Complexity of Mean Flow Time Scheduling Problems with Release Times
We study the problem of preemptive scheduling n jobs with given release times
on m identical parallel machines. The objective is to minimize the average flow
time. We show that when all jobs have equal processing times then the problem
can be solved in polynomial time using linear programming. Our algorithm can
also be applied to the open-shop problem with release times and unit processing
times. For the general case (when processing times are arbitrary), we show that
the problem is unary NP-hard.Comment: Subsumes and replaces cs.DS/0412094 and "Complexity of mean flow time
scheduling problems with release dates" by P.B, S.
Constraint satisfaction adaptive neural network and heuristics combined approaches for generalized job-shop scheduling
Copyright @ 2000 IEEEThis paper presents a constraint satisfaction adaptive neural network, together with several heuristics, to solve the generalized job-shop scheduling problem, one of NP-complete constraint satisfaction problems. The proposed neural network can be easily constructed and can adaptively adjust its weights of connections and biases of units based on the sequence and resource constraints of the job-shop scheduling problem during its processing. Several
heuristics that can be combined with the neural network are also presented. In the combined approaches, the neural network is used to obtain feasible solutions, the heuristic algorithms are used to improve
the performance of the neural network and the quality of the obtained solutions. Simulations have shown that the proposed
neural network and its combined approaches are efficient with respect to the quality of solutions and the solving speed.This work was supported by the Chinese National Natural Science Foundation under Grant 69684005 and the Chinese National High-Tech Program under Grant 863-511-9609-003, the EPSRC under Grant GR/L81468
New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria
In this paper, we are interested in parallel identical machine scheduling
problems with preemption and release dates in case of a regular criterion to be
minimized. We show that solutions having a permutation flow shop structure are
dominant if there exists an optimal solution with completion times scheduled in
the same order as the release dates, or if there is no release date. We also
prove that, for a subclass of these problems, the completion times of all jobs
can be ordered in an optimal solution. Using these two results, we provide new
results on polynomially solvable problems and hence refine the boundary between
P and NP for these problems
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
Polynomial-time approximation schemes for scheduling problems with time lags
We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the number of machines and the ratio between the largest time lag and the smallest positive operation time. These classes constitute the first PTAS results for scheduling problems with time lags
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