scholarly journals A New Approach to Online Scheduling: Approximating the Optimal Competitive Ratio

2013 ◽  
Author(s):  
Elisabeth Günther ◽  
Olaf Maurer ◽  
Nicole Megow ◽  
Andreas Wiese
Keyword(s):  
Competitive Ratio ◽  
Online Scheduling ◽  
New Approach

Approximating the Optimal Algorithm for Online Scheduling Problems via Dynamic Programming

2015 ◽  
Vol 32 (01) ◽  
pp. 1540011 ◽  
Author(s):  
Lin Chen ◽  
Deshi Ye ◽  
Guochuan Zhang
Keyword(s):  
Dynamic Programming ◽  
Competitive Ratio ◽  
Optimal Algorithm ◽  
Dynamic Programming Algorithm ◽  
Online Scheduling ◽  
Programming Algorithm ◽  
Scheduling Problems ◽  
New Approach ◽  
Discrete Algorithms ◽  
Online Problems

Very recently Günther et al. [E. Günther, O. Maurer, N. Megow and A. Wiese (2013). A new approach to online scheduling: Approximating the optimal competitive ratio. In Proc. 24th Annual ACM-SIAM Symp. Discrete Algorithms (SODA).] initiate a new systematic way of studying online problems by introducing the competitive ratio approximation scheme (simplified as competitive schemes in this paper), which is a class of algorithms {Aϵ|ϵ > 0} with a competitive ratio at most ρ*(1 + ϵ), where ρ* is the best possible competitive ratio over all online algorithms. Along this line, Günther et al. [E. Günther, O. Maurer, N. Megow and A. Wiese (2013). A new approach to online scheduling: Approximating the optimal competitive ratio. In Proc. 24th Annual ACM-SIAM Symp. Discrete Algorithms (SODA).] provide competitive schemes for several online over time scheduling problems like Qm|rj, (pmtn)|∑wjcj, while the running times are polynomial if the number of machines is a constant. In this paper, we consider the classical online scheduling problems, where jobs arrive in a list. We present competitive schemes for Rm‖C max and [Formula: see text], where the running times are polynomial if the number of machines is a constant. Specifically, we are able to derive a competitive scheme for P‖C max which runs in polynomial time even if the number of machines is an input. Our method is novel and more efficient than that of Günther et al. [E. Günther, O. Maurer, N. Megow and A. Wiese (2013). A new approach to online scheduling: Approximating the optimal competitive ratio. In Proc. 24th Annual ACM-SIAM Symp. Discrete Algorithms (SODA).] Indeed, by utilizing the standard rounding technique for the off-line scheduling problems, we reformulate the online scheduling problem into a game on an infinite graph, through which we arrive at the following key point: Assuming that the best competitive ratio is ρ*, for any online algorithm there exists a list of a polynomial number of jobs showing that its competitive ratio is at least ρ* - O(ϵ). Interestingly such a result is achieved via a dynamic programming algorithm. Our framework is also applicable to other online problems.

ONLINE SCHEDULING OF DYNAMIC TREES

1995 ◽  
Vol 05 (04) ◽  
pp. 635-646 ◽  
Author(s):  
MICHAEL A. PALIS ◽  
JING-CHIOU LIOU ◽  
SANGUTHEVAR RAJASEKARAN ◽  
SUNIL SHENDE ◽  
DAVID S.L. WEI
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Scheduling Algorithm ◽  
Optimal Schedule ◽  
Online Scheduling ◽  
The Other ◽  
Static Case ◽  
Scheduling Problem ◽  
Dynamic Trees ◽  
Dynamic Tree

The scheduling problem for dynamic tree-structured task graphs is studied and is shown to be inherently more difficult than the static case. It is shown that any online scheduling algorithm, deterministic or randomized, has competitive ratio Ω((1/g)/ log d(1/g)) for trees with granularity g and degree at most d. On the other hand, it is known that static trees with arbitrary granularity can be scheduled to within twice the optimal schedule. It is also shown that the lower bound is tight: there is a deterministic online tree scheduling algorithm that has competitive ratio O((1/g)/ log d(1/g)). Thus, randomization does not help.

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.

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 SCHEDULING OF UNIT JOBS WITH BOUNDED IMPORTANCE RATIO

2005 ◽  
Vol 16 (03) ◽  
pp. 581-598 ◽  
Author(s):  
STANLEY P. Y. FUNG ◽  
FRANCIS Y. L. CHIN ◽  
HONG SHEN
Keyword(s):  
Quality Of Service ◽  
Competitive Ratio ◽  
Online Scheduling ◽  
Release Time ◽  
Scheduling Problem ◽  
Network Switches ◽  
Unit Processing

We consider the following online scheduling problem. We are given a set of jobs, each having an integral release time and deadline, unit processing length, and a nonnegative real weight. In each time unit one job is to be scheduled, and the objective is to maximize the total value (weight) obtained by scheduling the jobs. This problem arises in the scheduling of packets in network switches supporting quality-of-service (QoS). Previous algorithms for this problem are 2-competitive. In this paper we propose a new algorithm that achieves an improved competitive ratio when the importance ratio is bounded. Specifically, for job weights within the range [1..B], our algorithm is 2 - 1/(⌈ lg B⌉ + 2)-competitive, and the bound is tight.

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.

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].

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.

scholarly journals Efficient Mechanism Design for Online Scheduling

2016 ◽  
Vol 56 ◽  
pp. 429-461 ◽  
Author(s):  
Xujin Chen ◽  
Xiaodong Hu ◽  
Tie-Yan Liu ◽  
Weidong Ma ◽  
Tao Qin ◽  
...  
Keyword(s):  
Social Welfare ◽  
Mechanism Design ◽  
Lower Bounds ◽  
Competitive Analysis ◽  
Competitive Ratio ◽  
Online Scheduling ◽  
Constant Factor ◽  
Release Time ◽  
Incentive Compatible ◽  
Unequal Length

This paper concerns the mechanism design for online scheduling in a strategic setting. In this setting, each job is owned by a self-interested agent who may misreport the release time, deadline, length, and value of her job, while we need to determine not only the schedule of the jobs, but also the payment of each agent. We focus on the design of incentive compatible (IC) mechanisms, and study the maximization of social welfare (i.e., the aggregated value of completed jobs) by competitive analysis. We first derive two lower bounds on the competitive ratio of any deterministic IC mechanism to characterize the landscape of our research. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for both the preemption-restart model and the preemption-resume model. We show the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within a constant factor) for unequal-length jobs.

Sign in / Sign up

Export Citation Format

Share Document