scholarly journals Efficient Mechanism Design for Online Scheduling (Extended Abstract)

2017 ◽  
Author(s):  
Xujin Chen ◽  
Xiaodong Hu ◽  
Tie-Yan Liu ◽  
Weidong Ma ◽  
Tao Qin ◽  
...  
Keyword(s):  
Mechanism Design ◽  
Lower Bounds ◽  
Competitive Ratio ◽  
Online Scheduling ◽  
Equal Length ◽  
The Other ◽  
Release Time ◽  
Incentive Compatible ◽  
Small Constant ◽  
Unequal Length

This work 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: one bound is 5, which holds for equal-length jobs; the other bound is $\frac{\kappa}{\ln\kappa}+1-o(1)$, which holds for unequal-length jobs, where $\kappa$ is the maximum ratio between lengths of any two jobs. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for two models: (1) In the preemption-restart model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal ratio of $(\frac{1}{(1-\epsilon)^2}+o(1)) \frac{\kappa}{\ln\kappa}$ for unequal-length jobs, where $0<\epsilon<1$ is a small constant; (2) In the preemption-resume model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within factor 2) for unequal-length jobs.

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.

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.

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 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].

scholarly journals Online Non-preemptive Scheduling on Unrelated Machines with Rejections

2021 ◽  
Vol 8 (2) ◽  
pp. 1-22
Author(s):  
Giorgio Lucarelli ◽  
Benjamin Moseley ◽  
Nguyen Kim Thang ◽  
Abhinav Srivastav ◽  
Denis Trystram
Keyword(s):  
Lower Bounds ◽  
Competitive Ratio ◽  
Poor Performance ◽  
Flow Time ◽  
Theory And Practice ◽  
Worst Case Analysis ◽  
Preemptive Scheduling ◽  
Scheduling Problems ◽  
Worst Case ◽  
Small Constant

When a computer system schedules jobs there is typically a significant cost associated with preempting a job during execution. This cost can be incurred from the expensive task of saving the memory’s state or from loading data into and out of memory. Thus, it is desirable to schedule jobs non-preemptively to avoid the costs of preemption. There is a need for non-preemptive system schedulers for desktops, servers, and data centers. Despite this need, there is a gap between theory and practice. Indeed, few non-preemptive online schedulers are known to have strong theoretical guarantees. This gap is likely due to strong lower bounds on any online algorithm for popular objectives. Indeed, typical worst-case analysis approaches, and even resource-augmented approaches such as speed augmentation, result in all algorithms having poor performance guarantees. This article considers online non-preemptive scheduling problems in the worst-case rejection model where the algorithm is allowed to reject a small fraction of jobs. By rejecting only a few jobs, this article shows that the strong lower bounds can be circumvented. This approach can be used to discover algorithmic scheduling policies with desirable worst-case guarantees. Specifically, the article presents algorithms for the following three objectives: minimizing the total flow-time, minimizing the total weighted flow-time plus energy where energy is a convex function, and minimizing the total energy under the deadline constraints. The algorithms for the first two problems have a small constant competitive ratio while rejecting only a constant fraction of jobs. For the last problem, we present a constant competitive ratio without rejection. Beyond specific results, the article asserts that alternative models beyond speed augmentation should be explored to aid in the discovery of good schedulers in the face of the requirement of being online and non-preemptive.

scholarly journals On Computing Multilinear Polynomials Using Multi- r -ic Depth Four Circuits

2021 ◽  
Vol 13 (3) ◽  
pp. 1-21
Author(s):  
Suryajith Chillara
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Complexity Measure ◽  
Natural Question ◽  
Multilinear Polynomial ◽  
Arithmetic Circuit ◽  
Theory Of Computing ◽  
Small Constant ◽  
Multilinear Polynomials ◽  
The Individual

In this article, we are interested in understanding the complexity of computing multilinear polynomials using depth four circuits in which the polynomial computed at every node has a bound on the individual degree of r ≥ 1 with respect to all its variables (referred to as multi- r -ic circuits). The goal of this study is to make progress towards proving superpolynomial lower bounds for general depth four circuits computing multilinear polynomials, by proving better bounds as the value of r increases. Recently, Kayal, Saha and Tavenas (Theory of Computing, 2018) showed that any depth four arithmetic circuit of bounded individual degree r computing an explicit multilinear polynomial on n O (1) variables and degree d must have size at least ( n / r 1.1 ) Ω(√ d / r ) . This bound, however, deteriorates as the value of r increases. It is a natural question to ask if we can prove a bound that does not deteriorate as the value of r increases, or a bound that holds for a larger regime of r . In this article, we prove a lower bound that does not deteriorate with increasing values of r , albeit for a specific instance of d = d ( n ) but for a wider range of r . Formally, for all large enough integers n and a small constant η, we show that there exists an explicit polynomial on n O (1) variables and degree Θ (log 2 n ) such that any depth four circuit of bounded individual degree r ≤ n η must have size at least exp(Ω(log 2 n )). This improvement is obtained by suitably adapting the complexity measure of Kayal et al. (Theory of Computing, 2018). This adaptation of the measure is inspired by the complexity measure used by Kayal et al. (SIAM J. Computing, 2017).

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

The randomized communication complexity of revenue maximization

2021 ◽  
Vol 19 (2) ◽  
pp. 75-83
Author(s):  
Aviad Rubinstein ◽  
Junyao Zhao
Keyword(s):  
Lower Bounds ◽  
Communication Complexity ◽  
Social Choice Rule ◽  
Valuation Function ◽  
Optimal Auctions ◽  
Incentive Compatible ◽  
First Approximation ◽  
Exponential Separation ◽  
Open Question

We study the communication complexity of incentive compatible auction-protocols between a monopolist seller and a single buyer with a combinatorial valuation function over n items [Rubinstein and Zhao 2021]. Motivated by the fact that revenue-optimal auctions are randomized [Thanassoulis 2004; Manelli and Vincent 2010; Briest et al. 2010; Pavlov 2011; Hart and Reny 2015] (as well as by an open problem of Babaioff, Gonczarowski, and Nisan [Babaioff et al. 2017]), we focus on the randomized communication complexity of this problem (in contrast to most prior work on deterministic communication). We design simple, incentive compatible, and revenue-optimal auction-protocols whose expected communication complexity is much (in fact infinitely) more efficient than their deterministic counterparts. We also give nearly matching lower bounds on the expected communication complexity of approximately-revenue-optimal auctions. These results follow from a simple characterization of incentive compatible auction-protocols that allows us to prove lower bounds against randomized auction-protocols. In particular, our lower bounds give the first approximation-resistant, exponential separation between communication complexity of incentivizing vs implementing a Bayesian incentive compatible social choice rule, settling an open question of Fadel and Segal [Fadel and Segal 2009].

scholarly journals A Competitive Ratio for Quantifying Competition Between Intercrops

1980 ◽  
Vol 16 (2) ◽  
pp. 117-125 ◽  
Author(s):  
R. W. Willey ◽  
M. R. Rao
Keyword(s):  
Competitive Ratio ◽  
Competitive Ability ◽  
Maximum Yield ◽  
The Other ◽  
Competitive Balance ◽  
Crop Competition

SUMMARYA simple competitive ratio (CR) is proposed as a measure of intercrop competition, to indicate the number of times by which one component crop is more competitive than the other. Intercropping data show that this CR term could be useful in (i) comparing the competitive ability of different crops, (ii) measuring competitive changes within a given combination, (iii) identifying which plant characters are associated with competitive ability, and (iv) determining what competitive balance between components is most likely to give maximum yield advantages.

Sign in / Sign up

Export Citation Format

Share Document