16,388 research outputs found
The Power of α-Points in Preemptive Single Machine Scheduling
We consider the NP-hard preemptive single machine scheduling problem to minimize the total weighted completion time subject to release dates. A natural extension of Smith's ratio rule is to preempt the currently active job whenever a new job arrives that has higher ratio of weight to processing time. We prove that the competitive ratio of this simple on-line algorithm is precisely~2. We also show that list scheduling in order of random α-points drawn from the same schedule results in an on-line algorithm with competitive ratio~4/3. Since its analysis relies on a well-known integer programming relaxation of the scheduling problem, the relaxation has performance guarantee~4/3 as well. On the other hand, we show that it is at best an~8/7-relaxation
Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling
This paper establishes performance guarantees for online algorithms that
schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the
expected total weighted completion time. Prior work on unrelated machine
scheduling with stochastic jobs was restricted to the offline case, and
required linear or convex programming relaxations for the assignment of jobs to
machines. The algorithms introduced in this paper are purely combinatorial. The
performance bounds are of the same order of magnitude as those of earlier work,
and depend linearly on an upper bound on the squared coefficient of variation
of the jobs' processing times. Specifically for deterministic processing times,
without and with release times, the competitive ratios are 4 and 7.216,
respectively. As to the technical contribution, the paper shows how dual
fitting techniques can be used for stochastic and nonpreemptive scheduling
problems.Comment: Preliminary version appeared in IPCO 201
Scheduling Jobs in Flowshops with the Introduction of Additional Machines in the Future
This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/expert-systems-with-applications/.The problem of scheduling jobs to minimize total weighted tardiness in flowshops,\ud
with the possibility of evolving into hybrid flowshops in the future, is investigated in\ud
this paper. As this research is guided by a real problem in industry, the flowshop\ud
considered has considerable flexibility, which stimulated the development of an\ud
innovative methodology for this research. Each stage of the flowshop currently has\ud
one or several identical machines. However, the manufacturing company is planning\ud
to introduce additional machines with different capabilities in different stages in the\ud
near future. Thus, the algorithm proposed and developed for the problem is not only\ud
capable of solving the current flow line configuration but also the potential new\ud
configurations that may result in the future. A meta-heuristic search algorithm based\ud
on Tabu search is developed to solve this NP-hard, industry-guided problem. Six\ud
different initial solution finding mechanisms are proposed. A carefully planned\ud
nested split-plot design is performed to test the significance of different factors and\ud
their impact on the performance of the different algorithms. To the best of our\ud
knowledge, this research is the first of its kind that attempts to solve an industry-guided\ud
problem with the concern for future developments
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
Lift-and-Round to Improve Weighted Completion Time on Unrelated Machines
We consider the problem of scheduling jobs on unrelated machines so as to
minimize the sum of weighted completion times. Our main result is a
-approximation algorithm for some fixed , improving upon the
long-standing bound of 3/2 (independently due to Skutella, Journal of the ACM,
2001, and Sethuraman & Squillante, SODA, 1999). To do this, we first introduce
a new lift-and-project based SDP relaxation for the problem. This is necessary
as the previous convex programming relaxations have an integrality gap of
. Second, we give a new general bipartite-rounding procedure that produces
an assignment with certain strong negative correlation properties.Comment: 21 pages, 4 figure
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