50,802 research outputs found
On robust online scheduling algorithms
While standard parallel machine scheduling is concerned with good assignments of jobs to machines, we aim to understand how the quality of an assignment is affected if the jobs' processing times are perturbed and therefore turn out to be longer (or shorter) than declared. We focus on online scheduling with perturbations occurring at any time, such as in railway systems when trains are late. For a variety of conditions on the severity of perturbations, we present bounds on the worst case ratio of two makespans. For the first makespan, we let the online algorithm assign jobs to machines, based on the non-perturbed processing times. We compute the makespan by replacing each job's processing time with its perturbed version while still sticking to the computed assignment. The second is an optimal offline solution for the perturbed processing times. The deviation of this ratio from the competitive ratio of the online algorithm tells us about the "price of perturbations”. We analyze this setting for Graham's algorithm, and among other bounds show a competitive ratio of 2 for perturbations decreasing the processing time of a job arbitrarily, and a competitive ratio of less than 2.5 for perturbations doubling the processing time of a job. We complement these results by providing lower bounds for any online algorithm in this setting. Finally, we propose a risk-aware online algorithm tailored for the possible bounded increase of the processing time of one job, and we show that this algorithm can be worse than Graham's algorithm in some case
Experimental Analysis of Algorithms for Coflow Scheduling
Modern data centers face new scheduling challenges in optimizing job-level
performance objectives, where a significant challenge is the scheduling of
highly parallel data flows with a common performance goal (e.g., the shuffle
operations in MapReduce applications). Chowdhury and Stoica introduced the
coflow abstraction to capture these parallel communication patterns, and
Chowdhury et al. proposed effective heuristics to schedule coflows efficiently.
In our previous paper, we considered the strongly NP-hard problem of minimizing
the total weighted completion time of coflows with release dates, and developed
the first polynomial-time scheduling algorithms with O(1)-approximation ratios.
In this paper, we carry out a comprehensive experimental analysis on a
Facebook trace and extensive simulated instances to evaluate the practical
performance of several algorithms for coflow scheduling, including the
approximation algorithms developed in our previous paper. Our experiments
suggest that simple algorithms provide effective approximations of the optimal,
and that the performance of our approximation algorithms is relatively robust,
near optimal, and always among the best compared with the other algorithms, in
both the offline and online settings.Comment: 29 pages, 8 figures, 11 table
Truth and Regret in Online Scheduling
We consider a scheduling problem where a cloud service provider has multiple
units of a resource available over time. Selfish clients submit jobs, each with
an arrival time, deadline, length, and value. The service provider's goal is to
implement a truthful online mechanism for scheduling jobs so as to maximize the
social welfare of the schedule. Recent work shows that under a stochastic
assumption on job arrivals, there is a single-parameter family of mechanisms
that achieves near-optimal social welfare. We show that given any such family
of near-optimal online mechanisms, there exists an online mechanism that in the
worst case performs nearly as well as the best of the given mechanisms. Our
mechanism is truthful whenever the mechanisms in the given family are truthful
and prompt, and achieves optimal (within constant factors) regret.
We model the problem of competing against a family of online scheduling
mechanisms as one of learning from expert advice. A primary challenge is that
any scheduling decisions we make affect not only the payoff at the current
step, but also the resource availability and payoffs in future steps.
Furthermore, switching from one algorithm (a.k.a. expert) to another in an
online fashion is challenging both because it requires synchronization with the
state of the latter algorithm as well as because it affects the incentive
structure of the algorithms. We further show how to adapt our algorithm to a
non-clairvoyant setting where job lengths are unknown until jobs are run to
completion. Once again, in this setting, we obtain truthfulness along with
asymptotically optimal regret (within poly-logarithmic factors)
Reallocation Problems in Scheduling
In traditional on-line problems, such as scheduling, requests arrive over
time, demanding available resources. As each request arrives, some resources
may have to be irrevocably committed to servicing that request. In many
situations, however, it may be possible or even necessary to reallocate
previously allocated resources in order to satisfy a new request. This
reallocation has a cost. This paper shows how to service the requests while
minimizing the reallocation cost. We focus on the classic problem of scheduling
jobs on a multiprocessor system. Each unit-size job has a time window in which
it can be executed. Jobs are dynamically added and removed from the system. We
provide an algorithm that maintains a valid schedule, as long as a sufficiently
feasible schedule exists. The algorithm reschedules only a total number of
O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from
the system, where n is the number of active jobs and Delta is the size of the
largest window.Comment: 9 oages, 1 table; extended abstract version to appear in SPAA 201
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