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

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

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

When Network Matters: Data Center Scheduling with Network Tasks

International audienceWe consider the placement of jobs inside a data center. Traditionally, this is done by a task orchestrator without taking into account network constraints. According to recent studies, network transfers represent up to 50% of the completion time of classical jobs. Thus, network resources must be considered when placing jobs in a data center. In this paper, we propose a new scheduling framework, introducing network tasks that need to be executed on network machines alongside traditional (CPU) tasks. The model takes into account the competition between communications for the network resources, which is not considered in the formerly proposed scheduling models with communication. Network transfers inside a data center can be easily modeled in our framework. As we show, classical algorithms do not efficiently handle a limited amount of network bandwidth. We thus propose new provably efficient algorithms with the goal of minimizing the makespan in this framework. We show their efficiency and the importance of taking into consideration network capacity through extensive simulations on workflows built from Google data center traces

Edge computing infrastructure for 5G networks: a placement optimization solution

This thesis focuses on how to optimize the placement of the Edge Computing infrastructure for upcoming 5G networks. To this aim, the core contributions of this research are twofold: 1) a novel heuristic called Hybrid Simulated Annealing to tackle the NP-hard nature of the problem and, 2) a framework called EdgeON providing a practical tool for real-life deployment optimization. In more detail, Edge Computing has grown into a key solution to 5G latency, reliability and scalability requirements. By bringing computing, storage and networking resources to the edge of the network, delay-sensitive applications, location-aware systems and upcoming real-time services leverage the benefits of a reduced physical and logical path between the end-user and the data or service host. Nevertheless, the edge node placement problem raises critical concerns regarding deployment and operational expenditures (i.e., mainly due to the number of nodes to be deployed), current backhaul network capabilities and non-technical placement limitations. Common approaches to the placement of edge nodes are based on: Mobile Edge Computing (MEC), where the processing capabilities are deployed at the Radio Access Network nodes and Facility Location Problem variations, where a simplistic cost function is used to determine where to optimally place the infrastructure. However, these methods typically lack the flexibility to be used for edge node placement under the strict technical requirements identified for 5G networks. They fail to place resources at the network edge for 5G ultra-dense networking environments in a network-aware manner. This doctoral thesis focuses on rigorously defining the Edge Node Placement Problem (ENPP) for 5G use cases and proposes a novel framework called EdgeON aiming at reducing the overall expenses when deploying and operating an Edge Computing network, taking into account the usage and characteristics of the in-place backhaul network and the strict requirements of a 5G-EC ecosystem. The developed framework implements several placement and optimization strategies thoroughly assessing its suitability to solve the network-aware ENPP. The core of the framework is an in-house developed heuristic called Hybrid Simulated Annealing (HSA), seeking to address the high complexity of the ENPP while avoiding the non-convergent behavior of other traditional heuristics (i.e., when applied to similar problems). The findings of this work validate our approach to solve the network-aware ENPP, the effectiveness of the heuristic proposed and the overall applicability of EdgeON. Thorough performance evaluations were conducted on the core placement solutions implemented revealing the superiority of HSA when compared to widely used heuristics and common edge placement approaches (i.e., a MEC-based strategy). Furthermore, the practicality of EdgeON was tested through two main case studies placing services and virtual network functions over the previously optimally placed edge nodes. Overall, our proposal is an easy-to-use, effective and fully extensible tool that can be used by operators seeking to optimize the placement of computing, storage and networking infrastructure at the users’ vicinity. Therefore, our main contributions not only set strong foundations towards a cost-effective deployment and operation of an Edge Computing network, but directly impact the feasibility of upcoming 5G services/use cases and the extensive existing research regarding the placement of services and even network service chains at the edge

Deep Learning for Head Pose Estimation: A Survey

Head pose estimation (HPE) is an active and popular area of research. Over the years, many approaches have constantly been developed, leading to a progressive improvement in accuracy; nevertheless, head pose estimation remains an open research topic, especially in unconstrained environments. In this paper, we will review the increasing amount of available datasets and the modern methodologies used to estimate orientation, with a special attention to deep learning techniques. We will discuss the evolution of the feld by proposing a classifcation of head pose estimation methods, explaining their advantages and disadvantages, and highlighting the diferent ways deep learning techniques have been used in the context of HPE. An in-depth performance comparison and discussion is presented at the end of the work. We also highlight the most promising research directions for future investigations on the topic

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