New Competitive Semi-online Scheduling Algorithms for Small Number of Identical Machines

Design and analysis of constant competitive deterministic semi-online algorithms for the multi-processor scheduling problem with small number of identical machines have gained significant research interest in the last two decades. In the semi-online scheduling problem for makespan minimization, we are given a sequence of independent jobs one by one in order and upon arrival, each job must be allocated to a machine with prior knowledge of some Extra Piece of Information (EPI) about the future jobs. Researchers have designed multiple variants of semi-online scheduling algorithms with constant competitive ratios by considering one or more EPI. In this paper, we propose four new variants of competitive deterministic semi-online algorithms for smaller number of identical machines by considering two EPI such as Decr and Sum. We obtain improved upper bound and lower bound results on the competitive ratio for our proposed algorithms, which are comparable to the best known results in the literature. In two identical machines setting with known Sum, we show a tight bound of 1.33 on the competitive ratio by considering a sequence of equal size jobs. In the same setting we achieve a lower bound of 1.04 and an upper bound of 1.16 by considering Sum and a sequence of jobs arriving in order of decreasing sizes. For three identical machines setting with known Decr and Sum, we show a lower bound of 1.11 on the competitive ratio. In this setting, we obtain an upper bound of 1.5 for scheduling a sequence of equal size jobs and achieves an upper bound of 1.2 by considering a sequence of decreasing size jobs. Further we develop an improved competitive algorithm with an upper bound of 1.11 on the competitive ratio.Comment: 24 Pages, 4 Table

Semi-online Scheduling: A Survey

In online scheduling, jobs are available one by one and each job must be scheduled irrevocably before the availability of the next job. Semi-online scheduling is a relaxed variant of online scheduling, where an additional memory in terms of buffer or an Extra Piece of Information(EPI) is provided along with input data. The EPI may include one or more of the parameter(s) such as size of the largest job, total size of all jobs, arrival sequence of the jobs, optimum makespan value or range of job's processing time. A semi-online scheduling algorithm was first introduced in 1997 by Kellerer et al. They envisioned semi-online scheduling as a practically significant model and obtained improved results for $2$-identical machine setting. This paper surveys scholarly contributions in the design of semi-online scheduling algorithms in parallel machine models such as identical and uniformly related by considering job's processing formats such as preemptive and non-preemptive with the optimality criteria such as Min-Max and Max-Min. The main focus is to present state of the art competitive analysis results of well-known semi-online scheduling algorithms in a chronological overview. The survey first introduces the online and semi-online algorithmic frameworks for the multi-processor scheduling problem with important applications and research motivation, followed by a taxonomy for semi-online scheduling. Fifteen well-known semi-online scheduling algorithms are stated. Important competitive analysis results are presented in a chronological way by highlighting the critical ideas and intuition behind the results. An evolution time-line of semi-online scheduling setups and a classification of the references based on EPI are outlined. Finally, the survey concludes with the exploration of some of the interesting research challenges and open problems.Comment: 48 pages, 7 figures and 10 table

Online Scheduling with Makespan Minimization: State of the Art Results, Research Challenges and Open Problems

Online scheduling has been a well studied and challenging research problem over the last five decades since the pioneering work of Graham with immense practical significance in various applications such as interactive parallel processing, routing in communication networks, distributed data management, client-server communications, traffic management in transportation, industrial manufacturing and production. In this problem, a sequence of jobs is received one by one in order by the scheduler for scheduling over a number of machines. On arrival of a job, the scheduler assigns the job irrevocably to a machine before the availability of the next job with an objective to minimize the completion time of the scheduled jobs. This paper highlights the state of the art contributions for online scheduling of a sequence of independent jobs on identical and uniform related machines with a special focus on preemptive and non-preemptive processing formats by considering makespan minimization as the optimality criterion. We present the fundamental aspects of online scheduling from a beginner's perspective along with a background of general scheduling framework. Important competitive analysis results obtained by well-known deterministic and randomized online scheduling algorithms in the literature are presented along with research challenges and open problems. Two of the emerging recent trends such as resource augmentation and semi-online scheduling are discussed as a motivation for future research work.Comment: 37 pages, 13 Tables, Submitted to Computer Science Revie