Some topics on deterministic scheduling problems

Sequencing and scheduling problems are motivated by allocation of limited resources over time. The goal is to find an optimal allocation where optimality is defined by some problem specific objectives. This dissertation considers the scheduling of a set of ri tasks, with precedence constraints, on m \u3e= 1 identical and parallel processors so as to minimize the makespan. Specifically, it considers the situation where tasks, along with their precedence constraints, are released at different times, and the scheduler has to make scheduling decisions without knowledge of future releases. Both preemptive and nonpreemptive schedules are considered. This dissertation shows that optimal online algorithms exist for some cases, while for others it is impossible to have one. The results give a sharp boundary delineating the possible and the impossible cases. Then an O(n log n)-time implementation is given for the algorithm which solves P|pj = 1, rj, outtree| ΣCj and P|pmtn, pj=1,rj,outtree|ΣCj. A fundamental problem in scheduling theory is that of scheduling a set of n unit-execution-time (UET) tasks, with precedence constraints, on m \u3e 1 parallel and identical processors so as to minimize the mean flow time. For arbitrary precedence constraints, this dissertation gives a 2-approximation algorithm. For intrees, a 1.5-approximation algorithm is given. Six dual criteria problems are also considered in this dissertation. Two open problems are first solved. Both problems are single machine scheduling problems with the number of tardy jobs as the primary criterion and with the total completion time and the total tardiness as the secondary criterion, respectively. Both problems are shown to be NP-hard. Then it focuses on bi-criteria scheduling problems involving the number of tardy jobs, the maximum weighted tardiness and the maximum tardiness. NP-hardness proofs are given for the scheduling problems when the number of tardy jobs is the primary criterion and the maximum weighted tardiness is the secondary criterion, or vice versa. It then considers complexity relationships between the various problems, gives polynomial-time algorithms for some special cases, and proposes fast heuristics for the general case

Scheduling task systems with resources.

Thesis. 1980. Ph.D.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.Vita.Bibliography: leaves 144-145.Ph.D

Algorithms for minimizing maximum lateness with unit length tasks and resource constraints

AbstractThe problem we consider is that of scheduling n unit length tasks on identical processors in the presence of additional scarce resources. The objective is to minimize maximum lateness. It has been known for some time that the problem is NP-hard even for two processors and one resource type. In the present paper we show that the problem can be solved in O(n log n) time, even for an arbitrary number of resources if the instance of the problem has the saturation property (i.e., no resource unit is idle in an optimal schedule). For the more general problem without saturation, two heuristic algorithms and a branch and bound approach are proposed. The results of computational tests of the above methods are also reported

Scheduling with Communication Delays

International audiencehanbook on ordonnancemen

Four decades of research on the open-shop scheduling problem to minimize the makespan

One of the basic scheduling problems, the open-shop scheduling problem has a broad range of applications across different sectors. The problem concerns scheduling a set of jobs, each of which has a set of operations, on a set of different machines. Each machine can process at most one operation at a time and the job processing order on the machines is immaterial, i.e., it has no implication for the scheduling outcome. The aim is to determine a schedule, i.e., the completion times of the operations processed on the machines, such that a performance criterion is optimized. While research on the problem dates back to the 1970s, there have been reviving interests in the computational complexity of variants of the problem and solution methodologies in the past few years. Aiming to provide a complete road map for future research on the open-shop scheduling problem, we present an up-to-date and comprehensive review of studies on the problem that focuses on minimizing the makespan, and discuss potential research opportunities

Some combinational optimization problems on radio network communication and machine scheduling

The combinatorial optimization problems coming from two areas are studied in this dissertation: network communication and machine scheduling. In the network communication area, the complexity of distributed broadcasting and distributed gossiping is studied in the setting of random networks. Two different models are considered: one is random geometric networks, the main model used to study properties of sensor and ad-hoc networks, where ri points are randomly placed in a unit square and two points are connected by an edge if they are at most a certain fixed distance r from each other. The other model is the so-called line-of-sight networks, a new network model introduced recently by Frieze et al. (SODA\u2707). The nodes in this model are randomly placed (with probability p) on an n x n grid and a node can communicate with all the nodes that are in at most a certain fixed distance r and which are in the same row or column. It can be shown that in many scenarios of both models, the random structure of these networks makes it possible to perform distributed gossiping in asymptotically optimal time 0(D), where D is the diameter of the network. The simulation results show that most algorithms especially the randomized algorithm works very fast in practice. In the scheduling area, the first problem is online scheduling a set of equal processing time tasks with precedence constraints so as to minimize the makespan. It can be shown that Hu \u27s algorithm yields an asymptotic competitive ratio of 3/2 for intree precedence constraints and an asymptotic competitive ratio of 1 for outtree precedences, and Coffinan-Graham algorithm yields an asymptotic competitive ratio of 1 for arbitrary precedence constraints and two machines.The second scheduling problem is the integrated production and delivery scheduling with disjoint windows. In this problem, each job is associated with a time window, and a profit. A job must be finished within its time window to get the profit. The objective is to pick a set ofjobs and schedule them to get the maximum total profit. For a single machine and unit profit, an optimal algorithm is proposed. For a single machine and arbitrary profit, a fully polynomial time approximation scheme(FPTAS) is proposed. These algorithms can be extended to multiple machines with approximation ratio less than e/(e - 1). The third scheduling problem studied in this dissertation is the preemptive scheduling algorithms with nested and inclusive processing set restrictions. The objective is to minimize the makespan of the schedule. It can be shown that there is no optimal online algorithm even for the case of inclusive processing set. Then a linear time optimal algorithm is given for the case of nested processing set, where all jobs are available for processing at time t = 0. A more complicated algorithm with running time 0(n log ri) is given that produces not only optimal but also maximal schedules. When jobs have different release times, an optimal algorithm is given for the nested case and a faster optimal algorithm is given for the inclusive processing set case

A Survey of Pipelined Workflow Scheduling: Models and Algorithms

International audienceA large class of applications need to execute the same workflow on different data sets of identical size. Efficient execution of such applications necessitates intelligent distribution of the application components and tasks on a parallel machine, and the execution can be orchestrated by utilizing task-, data-, pipelined-, and/or replicated-parallelism. The scheduling problem that encompasses all of these techniques is called pipelined workflow scheduling, and it has been widely studied in the last decade. Multiple models and algorithms have flourished to tackle various programming paradigms, constraints, machine behaviors or optimization goals. This paper surveys the field by summing up and structuring known results and approaches