Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems

Non-Preemptive Scheduling on Machines with Setup Times

Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that runs in time polynomial in n, m and k and computes a solution with an approximation factor that can be made arbitrarily close to 3/2.Comment: A conference version of this paper has been accepted for publication in the proceedings of the 14th Algorithms and Data Structures Symposium (WADS

Heuristics Techniques for Scheduling Problems with Reducing Waiting Time Variance

In real computational world, scheduling is a decision making process. This is nothing but a systematic schedule through which a large numbers of tasks are assigned to the processors. Due to the resource limitation, creation of such schedule is a real challenge. This creates the interest of developing a qualitative scheduler for the processors. These processors are either single or parallel. One of the criteria for improving the efficiency of scheduler is waiting time variance (WTV). Minimizing the WTV of a task is a NP-hard problem. Achieving the quality of service (QoS) in a single or parallel processor by minimizing the WTV is a problem of task scheduling. To enhance the performance of a single or parallel processor, it is required to develop a stable and none overlap scheduler by minimizing WTV. An automated scheduler\u27s performance is always measured by the attributes of QoS. One of the attributes of QoS is ‘Timeliness’. First, this chapter presents the importance of heuristics with five heuristic-based solutions. Then applies these heuristics on 1‖WTV minimization problem and three heuristics with a unique task distribution mechanism on Qm|prec|WTV minimization problem. The experimental result shows the performance of heuristic in the form of graph for consonant problems

Scheduling reentrant jobs on parallel machines with a remote server

This paper explores a specific combinatorial problem relating to re-entrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem is inspired by the logistics of a semi-automated micro-biology laboratory. The testing programme in the laboratory corresponds roughly to a hybrid flowshop, whose bottleneck stage is the subject of study. We demonstrate the NP-hard nature of the problem, and provide various structural features. A heuristic is developed and tested on randomly generated benchmark data. Results indicate solutions reliably within 1.5% of optimum. We also provide a greedy 2-approximation algorithm. Test on real-life data from the microbiology laboratory indicate a 20% saving relative to current practice, which is more than can be achieved currently with 3 instead of 2 people staffing the primary machines

Energy-aware scheduling of bag-of-tasks applications on master-worker platforms

International audienceWe consider the problem of scheduling an application composed of independent tasks on a fully heterogeneous master-worker platform with communication costs. We introduce a bi-criteria approach aiming at maximizing the throughput of the application while minimizing the energy consumed by participating resources. Assuming arbitrary super-linear power consumption laws, we investigate different models, with energy overheads and memory constraints. Building upon closed-form expressions for the uni-processor case, we derive asymptotically optimal solutions for all models