Improved Algorithms for Online Scheduling of Malleable Parallel Jobs on Two Identical Machines

2015 ◽  
Vol 32 (05) ◽  
pp. 1550034
Author(s):  
Hao Zhou ◽  
Ping Zhou ◽  
Yiwei Jiang
Keyword(s):  
Execution Time ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Setup Time ◽  
Online Scheduling ◽  
Parallel Jobs ◽  
Identical Machines ◽  
Maximum Completion Time ◽  
One Machine ◽  
Two Machines

This paper addresses online scheduling of malleable parallel jobs to minimize the maximum completion time, i.e., makespan. It is assumed that the execution time of a job Jj with processing time pj is pj/k + (k-1)c if the job is assigned to k machines, where c > 0 is a constant setup time. We consider online algorithms for the scheduling problem on two identical machines. Namely, the job Jj can be processed on one machine with execution time pj or alternatively two machines in parallel with execution time pj/2+c. For the asymptotical competitive ratio, we provide an improved online algorithm with makespan no more than (3/2)C* +c/2, where C* is the optimal makespan. For the strict competitive ratio, we propose an online algorithm with competitive ratio of 1.54, which is close to the lower bound of 1.5.

ONLINE SCHEDULING OF PARALLEL JOBS WITH BOUNDED PROCESSING TIMES ON TWO MACHINES

2010 ◽  
Vol 02 (03) ◽  
pp. 425-432
Author(s):  
MING LIU ◽  
YINFENG XU ◽  
CHENGBIN CHU ◽  
FEIFENG ZHENG
Keyword(s):  
Competitive Ratio ◽  
Time Slot ◽  
Online Scheduling ◽  
Processing Times ◽  
Parallel Jobs ◽  
Simultaneous Processing ◽  
Bounded Processing Times ◽  
Two Machines ◽  
The Greedy Algorithm ◽  
Better Than

We study the problem of online scheduling parallel jobs with bounded processing times on 2 machines, and the objective is to minimize makespan. A parallel job requires simultaneous processing on a pre-specified, job-dependent number of machines. The problem is online in the sense that jobs are presented one by one. Once a job is presented, we must irrevocably assign it to some time slot before the next one shows up. We investigate the case where the processing times of jobs are bounded within interval [a, αa] where a > 0 and α > 1. We first prove a lower bound of competitive ratios for online algorithms equal [Formula: see text] when α ≥ 2 and [Formula: see text] when 1 < α < 2, respectively. We further prove that the Greedy algorithm proposed in Chan et al. (2008) is [Formula: see text]-competitive in the case but it cannot be better than [Formula: see text]-competitive. The results imply that when 1 < α < 2 Greedy has a competitive ratio better than 2, which is the competitive ratio of Greedy in the case without processing time bound.

ONLINE SCHEDULING OF MIXED CPU-GPU JOBS

2014 ◽  
Vol 25 (06) ◽  
pp. 745-761 ◽  
Author(s):  
LIN CHEN ◽  
DESHI YE ◽  
GUOCHUAN ZHANG
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Competitive Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Identical Machines ◽  
The One

We consider the online scheduling problem in a CPU-GPU cluster. In this problem there are two sets of processors, the CPU processors and the GPU processors. Each job has two distinct processing times, one for the CPU processor and the other for the GPU processor. Once a job is released, a decision should be made immediately about which processor it should be assigned to. The goal is to minimize the makespan, i.e., the largest completion time among all the processors. Such a problem could be seen as an intermediate model between the scheduling problem on identical machines and unrelated machines. We provide a 3.85-competitive online algorithm for this problem and show that no online algorithm exists with competitive ratio strictly less than 2. We also consider two special cases of this problem, the balanced case where the number of CPU processors equals to that of GPU processors, and the one-sided case where there is only one CPU or GPU processor. For the balanced case, we first provide a simple 3-competitive algorithm, and then a better algorithm with competitive ratio of 2.732 is derived. For the one-sided case, a 3-competitive algorithm is given.

scholarly journals Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Hailing Liu ◽  
Long Wan ◽  
Zhigang Yan ◽  
Jinjiang Yuan
Keyword(s):  
Positive Solution ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Equal Length ◽  
Delivery Time ◽  
Batch Machine ◽  
Time Scheduling ◽  
Work Done ◽  
Over Time

We consider the online (over time) scheduling of equal length jobs on a bounded parallel batch machine with batch capacitybto minimize the time by which all jobs have been delivered with limited restart. Here, “restart” means that a running batch may be interrupted, losing all the work done on it, and jobs in the interrupted batch are then released and become independently unscheduled jobs, called restarted jobs. “Limited restart” means that a running batch which contains some restarted jobs cannot be restarted again. Whenb=2, we propose a best possible online algorithmH(b=2)with a competitive ratio of1+α, whereαis the positive solution of2α(1+α)=1. Whenb≥3, we present a best possible online algorithmH(b≥3)with a competitive ratio of1+β, whereβis the positive solution ofβ(1+β)2=1.

ONLINE ALGORITHMS FOR SCHEDULING WITH MACHINE ACTIVATION COST

2007 ◽  
Vol 24 (02) ◽  
pp. 263-277 ◽  
Author(s):  
YONG HE ◽  
SHUGUANG HAN ◽  
YIWEI JIANG
Keyword(s):  
Lower Bound ◽  
Online Algorithms ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Identical Machines ◽  
Parallel Machine Scheduling Problem

In this paper, we consider a variant of the classical parallel machine scheduling problem. For this problem, we are given m potential identical machines to non-preemptively process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and activation cost of machines. We first present two optimal online algorithms with competitive ratios of 3/2 and 5/3 for m = 2, 3 cases, respectively. Then we present an online algorithm with a competitive ratio of at most 2 for general m ≥ 4, while the lower bound is 1.88.

Online Algorithms for Scheduling Unit Length Jobs on Unbounded Parallel-Batch Machines with Linearly Lookahead

2019 ◽  
Vol 36 (05) ◽  
pp. 1950024
Author(s):  
Chengwen Jiao ◽  
Jinjiang Yuan ◽  
Qi Feng
Keyword(s):  
Online Algorithms ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Positive Root ◽  
Unit Length ◽  
Online Scheduling ◽  
Time Interval ◽  
Steady Growth ◽  
Scheduling Model

In this paper, we propose a new online scheduling model with linear lookahead intervals, which has the character that at any time [Formula: see text], one can foresee the jobs that will coming in the time interval [Formula: see text] in which [Formula: see text]. In this new lookahead model, the length of the lookahead intervals are variable as the time going on and the number of jobs increasing, and has the tend of steady growth. In this paper, we consider online scheduling of unit length jobs on [Formula: see text] identical parallel-batch machines under this new lookahead model to minimize makespan. The batch capacity is unbounded, that is [Formula: see text]. We present an optimal online algorithm for [Formula: see text], and provide a best possible online algorithm of competitive ratio [Formula: see text] for [Formula: see text], where [Formula: see text] is the positive root of [Formula: see text].

Online Scheduling of Incompatible Family Jobs with Equal Length on an Unbounded Parallel-Batch Machine with Job Delivery

2018 ◽  
Vol 35 (04) ◽  
pp. 1850026
Author(s):  
Qijia Liu ◽  
Jinjiang Yuan
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Equal Length ◽  
Batch Machine ◽  
Job Delivery ◽  
Over Time

In this paper, we consider the online scheduling of incompatible family jobs with equal length on an unbounded parallel-batch machine with job delivery. The jobs arrive online over time and belong to [Formula: see text] incompatible job families, where [Formula: see text] is known in advance. The jobs are first processed in batches on an unbounded parallel-batch machine and then the completed jobs are delivered in batches by a vehicle with infinite capacity to their customers. The jobs from distinct families cannot be processed and delivered in the same batch. The objective is to minimize the maximum delivery completion time of the jobs. For this problem, we present an online algorithm with the best competitive ratio of [Formula: see text].

ONLINE MINIMUM MAKESPAN SCHEDULING WITH A BUFFER

2014 ◽  
Vol 25 (05) ◽  
pp. 525-536 ◽  
Author(s):  
NING DING ◽  
YAN LAN ◽  
XIN CHEN ◽  
GYÖRGY DÓSA ◽  
HE GUO ◽  
...  
Keyword(s):  
Competitive Ratio ◽  
Online Algorithm ◽  
Buffer Size ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
Minimum Makespan ◽  
Identical Machines ◽  
Better Than

In this paper we study an online minimum makespan scheduling problem with a reordering buffer. We obtain the following results: (i) for m > 51 identical machines, we give a 1.5-competitive online algorithm with a buffer of size ⌈1.5m⌉; (ii) for three identical machines, we give an optimal online algorithm with a buffer size six, better than the previous nine; (iii) for m uniform machines, using a buffer of size m, we improve the competitive ratio from 2 + ε to 2 − 1/m+ ε, where ε > 0 is sufficiently small and m is a constant.

scholarly journals Online Scheduling on a Single Machine with Grouped Processing Times

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qijia Liu ◽  
Long Wan ◽  
Lijun Wei
Keyword(s):  
Single Machine ◽  
Competitive Ratio ◽  
Processing Time ◽  
Online Algorithm ◽  
Arrival Time ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Over Time

We consider the online scheduling problem on a single machine with the assumption that all jobs have their processing times in[p,(1+α)p], wherep>0andα=(5-1)/2. All jobs arrive over time, and each job and its processing time become known at its arrival time. The jobs should be first processed on a single machine and then delivered by a vehicle to some customer. When the capacity of the vehicle is infinite, we provide an online algorithm with the best competitive ratio of(5+1)/2. When the capacity of the vehicle is finite, that is, the vehicle can deliver at mostcjobs at a time, we provide another best possible online algorithm with the competitive ratio of(5+1)/2.

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