1,657 research outputs found
Approximation schemes for preemptive weighted flow time
Am 27. Mai 2013 sprachen Stefan Klein, Andreas Kruse, Andreas Mergenthaler, Karlheinz Ruckriegel, Tim Tiefenbach und Gisela Trommsdorff in Mainz mit der Journalistin Doris Maull über die Auswirkungen des demografischen Wandels auf Lebenszufriedenheit und die Chancen, die sich aus diesen veränderten Bedingungen ergeben. Unseren Videomittschnitt aus der Akademie der Wissenschaften und der Literatur in Mainz finden Sie hier: http://vimeo.com/67364583 Wir wünschen viel Spass beim Ansehen! Geiste..
Minimum Makespan Multi-vehicle Dial-a-Ride
Dial a ride problems consist of a metric space (denoting travel time between
vertices) and a set of m objects represented as source-destination pairs, where
each object requires to be moved from its source to destination vertex. We
consider the multi-vehicle Dial a ride problem, with each vehicle having
capacity k and its own depot-vertex, where the objective is to minimize the
maximum completion time (makespan) of the vehicles. We study the "preemptive"
version of the problem, where an object may be left at intermediate vertices
and transported by more than one vehicle, while being moved from source to
destination. Our main results are an O(log^3 n)-approximation algorithm for
preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation
for its special case when there is no capacity constraint. We also show that
the approximation ratios improve by a log-factor when the underlying metric is
induced by a fixed-minor-free graph.Comment: 22 pages, 1 figure. Preliminary version appeared in ESA 200
Better Unrelated Machine Scheduling for Weighted Completion Time via Random Offsets from Non-Uniform Distributions
In this paper we consider the classic scheduling problem of minimizing total
weighted completion time on unrelated machines when jobs have release times,
i.e, using the three-field notation. For this
problem, a 2-approximation is known based on a novel convex programming (J. ACM
2001 by Skutella). It has been a long standing open problem if one can improve
upon this 2-approximation (Open Problem 8 in J. of Sched. 1999 by Schuurman and
Woeginger). We answer this question in the affirmative by giving a
1.8786-approximation. We achieve this via a surprisingly simple linear
programming, but a novel rounding algorithm and analysis. A key ingredient of
our algorithm is the use of random offsets sampled from non-uniform
distributions.
We also consider the preemptive version of the problem, i.e, . We again use the idea of sampling offsets from non-uniform
distributions to give the first better than 2-approximation for this problem.
This improvement also requires use of a configuration LP with variables for
each job's complete schedules along with more careful analysis. For both
non-preemptive and preemptive versions, we break the approximation barrier of 2
for the first time.Comment: 24 pages. To apper in FOCS 201
How Unsplittable-Flow-Covering helps Scheduling with Job-Dependent Cost Functions
Generalizing many well-known and natural scheduling problems, scheduling with
job-specific cost functions has gained a lot of attention recently. In this
setting, each job incurs a cost depending on its completion time, given by a
private cost function, and one seeks to schedule the jobs to minimize the total
sum of these costs. The framework captures many important scheduling objectives
such as weighted flow time or weighted tardiness. Still, the general case as
well as the mentioned special cases are far from being very well understood
yet, even for only one machine. Aiming for better general understanding of this
problem, in this paper we focus on the case of uniform job release dates on one
machine for which the state of the art is a 4-approximation algorithm. This is
true even for a special case that is equivalent to the covering version of the
well-studied and prominent unsplittable flow on a path problem, which is
interesting in its own right. For that covering problem, we present a
quasi-polynomial time -approximation algorithm that yields an
-approximation for the above scheduling problem. Moreover, for
the latter we devise the best possible resource augmentation result regarding
speed: a polynomial time algorithm which computes a solution with \emph{optimal
}cost at speedup. Finally, we present an elegant QPTAS for the
special case where the cost functions of the jobs fall into at most
many classes. This algorithm allows the jobs even to have up to many
distinct release dates.Comment: 2 pages, 1 figur
Preemptive scheduling on uniform parallel machines with controllable job processing times
In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan
Minimizing Flow-Time on Unrelated Machines
We consider some flow-time minimization problems in the unrelated machines
setting. In this setting, there is a set of machines and a set of jobs,
and each job has a machine dependent processing time of on machine
. The flow-time of a job is the total time the job spends in the system
(completion time minus its arrival time), and is one of the most natural
quality of service measure. We show the following two results: an
approximation algorithm for minimizing the
total-flow time, and an approximation for minimizing the maximum
flow-time. Here is the ratio of maximum to minimum job size. These are the
first known poly-logarithmic guarantees for both the problems.Comment: The new version fixes some typos in the previous version. The paper
is accepted for publication in STOC 201
Asymptotically Optimal Approximation Algorithms for Coflow Scheduling
Many modern datacenter applications involve large-scale computations composed
of multiple data flows that need to be completed over a shared set of
distributed resources. Such a computation completes when all of its flows
complete. A useful abstraction for modeling such scenarios is a {\em coflow},
which is a collection of flows (e.g., tasks, packets, data transmissions) that
all share the same performance goal.
In this paper, we present the first approximation algorithms for scheduling
coflows over general network topologies with the objective of minimizing total
weighted completion time. We consider two different models for coflows based on
the nature of individual flows: circuits, and packets. We design
constant-factor polynomial-time approximation algorithms for scheduling
packet-based coflows with or without given flow paths, and circuit-based
coflows with given flow paths. Furthermore, we give an -approximation polynomial time algorithm for scheduling circuit-based
coflows where flow paths are not given (here is the number of network
edges).
We obtain our results by developing a general framework for coflow schedules,
based on interval-indexed linear programs, which may extend to other coflow
models and objective functions and may also yield improved approximation bounds
for specific network scenarios. We also present an experimental evaluation of
our approach for circuit-based coflows that show a performance improvement of
at least 22% on average over competing heuristics.Comment: Fixed minor typo
The Geometry of Scheduling
We consider the following general scheduling problem: The input consists of n
jobs, each with an arbitrary release time, size, and a monotone function
specifying the cost incurred when the job is completed at a particular time.
The objective is to find a preemptive schedule of minimum aggregate cost. This
problem formulation is general enough to include many natural scheduling
objectives, such as weighted flow, weighted tardiness, and sum of flow squared.
Our main result is a randomized polynomial-time algorithm with an approximation
ratio O(log log nP), where P is the maximum job size. We also give an O(1)
approximation in the special case when all jobs have identical release times.
The main idea is to reduce this scheduling problem to a particular geometric
set-cover problem which is then solved using the local ratio technique and
Varadarajan's quasi-uniform sampling technique. This general algorithmic
approach improves the best known approximation ratios by at least an
exponential factor (and much more in some cases) for essentially all of the
nontrivial common special cases of this problem. Our geometric interpretation
of scheduling may be of independent interest.Comment: Conference version in FOCS 201
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