9,070 research outputs found
Some combinational optimization problems on radio network communication and machine scheduling
The combinatorial optimization problems coming from two areas are studied in this dissertation: network communication and machine scheduling.
In the network communication area, the complexity of distributed broadcasting and distributed gossiping is studied in the setting of random networks. Two different models are considered: one is random geometric networks, the main model used to study properties of sensor and ad-hoc networks, where ri points are randomly placed in a unit square and two points are connected by an edge if they are at most a certain fixed distance r from each other. The other model is the so-called line-of-sight networks, a new network model introduced recently by Frieze et al. (SODA\u2707). The nodes in this model are randomly placed (with probability p) on an n x n grid and a node can communicate with all the nodes that are in at most a certain fixed distance r and which are in the same row or column. It can be shown that in many scenarios of both models, the random structure of these networks makes it possible to perform distributed gossiping in asymptotically optimal time 0(D), where D is the diameter of the network. The simulation results show that most algorithms especially the randomized algorithm works very fast in practice.
In the scheduling area, the first problem is online scheduling a set of equal processing time tasks with precedence constraints so as to minimize the makespan. It can be shown that Hu \u27s algorithm yields an asymptotic competitive ratio of 3/2 for intree precedence constraints and an asymptotic competitive ratio of 1 for outtree precedences, and Coffinan-Graham algorithm yields an asymptotic competitive ratio of 1 for arbitrary precedence constraints and two machines.The second scheduling problem is the integrated production and delivery scheduling with disjoint windows. In this problem, each job is associated with a time window, and a profit. A job must be finished within its time window to get the profit. The objective is to pick a set ofjobs and schedule them to get the maximum total profit. For a single machine and unit profit, an optimal algorithm is proposed. For a single machine and arbitrary profit, a fully polynomial time approximation scheme(FPTAS) is proposed. These algorithms can be extended to multiple machines with approximation ratio less than e/(e - 1).
The third scheduling problem studied in this dissertation is the preemptive scheduling algorithms with nested and inclusive processing set restrictions. The objective is to minimize the makespan of the schedule. It can be shown that there is no optimal online algorithm even for the case of inclusive processing set. Then a linear time optimal algorithm is given for the case of nested processing set, where all jobs are available for processing at time t = 0. A more complicated algorithm with running time 0(n log ri) is given that produces not only optimal but also maximal schedules. When jobs have different release times, an optimal algorithm is given for the nested case and a faster optimal algorithm is given for the inclusive processing set case
Scheduling MapReduce Jobs under Multi-Round Precedences
We consider non-preemptive scheduling of MapReduce jobs with multiple tasks
in the practical scenario where each job requires several map-reduce rounds. We
seek to minimize the average weighted completion time and consider scheduling
on identical and unrelated parallel processors. For identical processors, we
present LP-based O(1)-approximation algorithms. For unrelated processors, the
approximation ratio naturally depends on the maximum number of rounds of any
job. Since the number of rounds per job in typical MapReduce algorithms is a
small constant, our scheduling algorithms achieve a small approximation ratio
in practice. For the single-round case, we substantially improve on previously
best known approximation guarantees for both identical and unrelated
processors. Moreover, we conduct an experimental analysis and compare the
performance of our algorithms against a fast heuristic and a lower bound on the
optimal solution, thus demonstrating their promising practical performance
Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling
We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed
Competitive-Ratio Approximation Schemes for Minimizing the Makespan in the Online-List Model
We consider online scheduling on multiple machines for jobs arriving
one-by-one with the objective of minimizing the makespan. For any number of
identical parallel or uniformly related machines, we provide a
competitive-ratio approximation scheme that computes an online algorithm whose
competitive ratio is arbitrarily close to the best possible competitive ratio.
We also determine this value up to any desired accuracy. This is the first
application of competitive-ratio approximation schemes in the online-list
model. The result proves the applicability of the concept in different online
models. We expect that it fosters further research on other online problems
Parallel Machine Scheduling with Nested Processing Set Restrictions and Job Delivery Times
The problem of scheduling jobs with delivery times on parallel machines is studied, where each job can only be processed on a specific subset of the machines called its processing set. Two distinct processing sets are either nested or disjoint; that is, they do not partially overlap. All jobs are available for processing at time 0. The goal is to minimize the time by which all jobs are delivered, which is equivalent to minimizing the maximum lateness from the optimization viewpoint. A list scheduling approach is analyzed and its approximation ratio of 2 is established. In addition, a polynomial time approximation scheme is derived
A deterministic truthful PTAS for scheduling related machines
Scheduling on related machines () is one of the most important
problems in the field of Algorithmic Mechanism Design. Each machine is
controlled by a selfish agent and her valuation can be expressed via a single
parameter, her {\em speed}. In contrast to other similar problems, Archer and
Tardos \cite{AT01} showed that an algorithm that minimizes the makespan can be
truthfully implemented, although in exponential time. On the other hand, if we
leave out the game-theoretic issues, the complexity of the problem has been
completely settled -- the problem is strongly NP-hard, while there exists a
PTAS \cite{HS88,ES04}.
This problem is the most well studied in single-parameter algorithmic
mechanism design. It gives an excellent ground to explore the boundary between
truthfulness and efficient computation. Since the work of Archer and Tardos,
quite a lot of deterministic and randomized mechanisms have been suggested.
Recently, a breakthrough result \cite{DDDR08} showed that a randomized truthful
PTAS exists. On the other hand, for the deterministic case, the best known
approximation factor is 2.8 \cite{Kov05,Kov07}.
It has been a major open question whether there exists a deterministic
truthful PTAS, or whether truthfulness has an essential, negative impact on the
computational complexity of the problem. In this paper we give a definitive
answer to this important question by providing a truthful {\em deterministic}
PTAS
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
Control-based Scheduling in a Distributed Stream Processing System
Stream processing systems receive continuous streams
of messages with raw information and produce streams
of messages with processed information. The utility of a
stream-processing system depends, in part, on the accuracy
and timeliness of the output. Streams in complex event processing
systems are processed on distributed systems; several
steps are taken on different processors to process each
incoming message, and messages may be enqueued between
steps. This paper deals with the problems of distributed dynamic
control of streams to optimize the total utility provided
by the system. A challenge of distributed control is
that timeliness of output depends only on the total end-toend
time and is otherwise independent of the delays at each
separate processor whereas the controller for each processor
takes action to control only the steps on that processor
and cannot directly control the entire network.
This paper identifies key problems in distributed control
and analyzes two scheduling algorithms that help in an initial
analysis of a difficult problem
An EPTAS for machine scheduling with bag-constraints
Machine scheduling is a fundamental optimization problem in computer science.
The task of scheduling a set of jobs on a given number of machines and
minimizing the makespan is well studied and among other results, we know that
EPTAS's for machine scheduling on identical machines exist. Das and Wiese
initiated the research on a generalization of makespan minimization, that
includes so called bag-constraints. In this variation of machine scheduling the
given set of jobs is partitioned into subsets, so called bags. Given this
partition a schedule is only considered feasible when on any machine there is
at most one job from each bag.
Das and Wiese showed that this variant of machine scheduling admits a PTAS.
We will improve on this result by giving the first EPTAS for the machine
scheduling problem with bag-constraints. We achieve this result by using new
insights on this problem and restrictions given by the bag-constraints. We show
that, to gain an approximate solution, we can relax the bag-constraints and
ignore some of the restrictions. Our EPTAS uses a new instance transformation
that will allow us to schedule large and small jobs independently of each other
for a majority of bags. We also show that it is sufficient to respect the
bag-constraint only among a constant number of bags, when scheduling large
jobs. With these observations our algorithm will allow for some conflicts when
computing a schedule and we show how to repair the schedule in polynomial-time
by swapping certain jobs around
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