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39
Scheduling multiprocessor tasks  An overview
 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
, 1996
"... Multiprocessor tasks require more than one processor at the same moment of time. This relatively new concept in scheduling theory emerged with the advent of parallel computing systems. In this work we present the state of the art for multiprocessor task scheduling. We show the rationale behind the c ..."
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Cited by 37 (3 self)
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Multiprocessor tasks require more than one processor at the same moment of time. This relatively new concept in scheduling theory emerged with the advent of parallel computing systems. In this work we present the state of the art for multiprocessor task scheduling. We show the rationale behind the concept of multiprocessor tasks. The standard threefield notation is extended to accommodate multiprocessor tasks. The main part of the work is presentation of the results in multiprocessor tasks scheduling both for parallel and for dedicated processors.
Tools for Multicoloring with Applications to Planar Graphs and Partial kTrees
, 2001
"... We study graph multicoloring problems, motivated by the scheduling of dependent jobs on multiple machines. In multicoloring problems, vertices have lengths which determine the number of colors they must receive, and the desired coloring can be either contiguous (nonpreemptive schedule) or arbitrary ..."
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Cited by 24 (6 self)
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We study graph multicoloring problems, motivated by the scheduling of dependent jobs on multiple machines. In multicoloring problems, vertices have lengths which determine the number of colors they must receive, and the desired coloring can be either contiguous (nonpreemptive schedule) or arbitrary (preemptive schedule). We consider both the sumofcompletion times measure, or the sum of the last color assigned to each vertex, as well as the more common makespan measure, or the number of colors used. In this paper, we study two fundamental classes of graphs: planar graphs and partial ktrees. For both classes, we give a polynomial time approximation scheme (PTAS) for the multicoloring sum, for both the preemptive and nonpreemptive cases. On the other hand, we show the problem to be strongly NPhard on planar graphs, even in the unweighted case, known as the Sum Coloring problem. For nonpreemptive multicoloring sum of partial ktrees, we obtain a fully polynomial time approximation scheme. This is based on a pseudopolynomial time algorithm that holds for a general class of cost functions. Finally, we give a PTAS for the makespan of a preemptive multicoloring of partial ktrees that uses only O(logn) preemptions. These results are based on several properties of multicolorings and tools for manipulating them, which may be of more general applicability.
Scheduling Independent Multiprocessor Tasks
, 1997
"... . We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm th ..."
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Cited by 23 (3 self)
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. We study the problem of scheduling a set of n independent multiprocessor tasks with prespecified processor allocations on a fixed number of processors. We propose a linear time algorithm that finds a schedule of minimum makespan in the preemptive model, and a linear time approximation algorithm that finds a schedule of length within a factor of (1 + ffl) of optimal in the nonpreemptive model. 1 Introduction A scheduling problem is usually given by a set T of n tasks, with an associated partial order which captures data dependencies between tasks, and a set Pm of m target processors. The goal is to assign tasks to processors and time steps so as to minimize an optimality criterion, for instance the makespan, i.e. the maximum completion time Cmax of any task. Depending on the model, tasks can be preempted or not. In the nonpreemptive model, a task once started has to be processed (until completion) without interruption. In the preemptive model, each task can be at no cost interrup...
Efficient file dissemination using peertopeer technology
, 2004
"... We consider a problem which is partially motivated by the BitTorrent protocol. Suppose that a large file is initially available only at some server and we desire to disseminate it amongst N end users in the least possible time. We suppose that the file is divided in M parts of equal size and that an ..."
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Cited by 15 (1 self)
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We consider a problem which is partially motivated by the BitTorrent protocol. Suppose that a large file is initially available only at some server and we desire to disseminate it amongst N end users in the least possible time. We suppose that the file is divided in M parts of equal size and that an end user may download a part from either the server or one of the peers who has previously downloaded it. Given constraints on the rates at which the server and peers can upload to one another, we seek a strategy that minimizes the time until all peers have downloaded the entire file. Assuming that there is a centralized controller who does the scheduling of the uploads, we show how to solve this problem by solving a finite number of linear programs. Making connections with the socalled ‘broadcasting problem’, we provide a complete solution of this problem when the capacities are all equal. We also carry out simulations to assess the performance of a natural randomized algorithm that operates under distributed control. We compare the performance of this algorithm in two different information scenarios with what can be achieved by centralized control.
Exchange of Messages of Different Sizes
 In IRREGULAR '98
"... In this paper, we study the exchange of messages among a set of processors linked through an interconnection network. We focus on general, nonuniform versions of alltoall (or complete) exchange problems in asynchronous systems with a linear cost model and messages of arbitrary sizes. We exten ..."
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Cited by 12 (4 self)
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In this paper, we study the exchange of messages among a set of processors linked through an interconnection network. We focus on general, nonuniform versions of alltoall (or complete) exchange problems in asynchronous systems with a linear cost model and messages of arbitrary sizes. We extend previous complexity results to show that the general asynchronous problems are NPcomplete. We present several approximation algorithms and determine which heuristics are best suited to several parallel systems. We conclude with experimental results that show that our algorithms outperform the native alltoall exchange algorithm on an IBM SP2 when the number of processors is odd.
OffLine and OnLine CallScheduling in Stars and Trees
 in Proceedings of the 23rd International Workshop on GraphTheoretic Concepts in Computer Science, WG ‘97, LNCS1335, SpringerVerlag
, 1997
"... . Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the callschedulin ..."
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Cited by 11 (2 self)
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. Given a communication network and a set of call requests, the goal is to find a minimum makespan schedule for the calls such that the sum of the bandwidth requirements of simultaneously active calls using the same link does not exceed the capacity of that link. In this paper the callscheduling problem is studied for star and tree networks. Lower and upper bounds on the worstcase performance of ListScheduling (LS) and variants of it are obtained for callscheduling with arbitrary bandwidth requirements and either unit call durations or arbitrary call durations. LS does not require advance knowledge of call durations and, hence, is an online algorithm. It has performance ratio (competitive ratio) at most 5 in star networks. A variant of LS for calls with unit durations is shown to have performance ratio at most 2 2 3 . In tree networks with n nodes, a variant of LS for calls with unit durations has performance ratio at most 6, and a variant for calls with arbitrary d...
ADAPTIVE LOCAL RATIO
, 2010
"... Local ratio is a wellknown paradigm for designing approximation algorithms for combinatorial optimization problems. At a very high level, a localratio algorithm first decomposes the input weight function w into a positive linear combination of simpler weight functions or models. Guided by this pr ..."
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Cited by 7 (3 self)
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Local ratio is a wellknown paradigm for designing approximation algorithms for combinatorial optimization problems. At a very high level, a localratio algorithm first decomposes the input weight function w into a positive linear combination of simpler weight functions or models. Guided by this process, a solution S is constructed such that S is αapproximate with respect to each model used in the decomposition. As a result, S is αapproximate under w as well. These models usually have a very simple structure that remains “unchanged ” throughout the execution of the algorithm. In this work we show that adaptively choosing a model from a richer spectrum of functions can lead to a better local ratio. Indeed, by turning the search for a good model into an optimization problem of its own, we get improved approximations for a data migration problem.
Routing and Scheduling File Transfers in PacketSwitched Networks
 Journal of Computing and Information
, 1994
"... Data traffic in networks has always been dominated by file transfers, an observation that has motivated previous work in scheduling file transfers. While these previous research contributions address file transfers, they do not address the special considerations required of packetswitched networks, ..."
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Cited by 6 (3 self)
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Data traffic in networks has always been dominated by file transfers, an observation that has motivated previous work in scheduling file transfers. While these previous research contributions address file transfers, they do not address the special considerations required of packetswitched networks, in particular the issues of routing and of simultaneous transmissions of files. In this paper, we generalize previous formulations of the problem to include routing and to allow for simultaneous transmissions of several files. A few theoretical results are presented. Keywords: Data transfers, File transfers, Scheduling, Routing, Large scale networking applications, NPCompleteness, Algorithms. 1 Introduction We consider the joint problem of scheduling and routing the transfers of very large files. Our research is motivated by the increasing size and ambition of future networking applications, many of which will result in the movement of very large amounts of data across networks. For examp...
Graph Coloring Problems and Their Applications in Scheduling
 IN PROC. JOHN VON NEUMANN PHD STUDENTS CONFERENCE
, 2004
"... Graph coloring and its generalizations are useful tools in modeling a wide variety of scheduling and assignment problems. In this paper we review several variants of graph coloring, such as precoloring extension, list coloring, multicoloring, minimum sum coloring, and discuss their applications i ..."
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Cited by 6 (0 self)
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Graph coloring and its generalizations are useful tools in modeling a wide variety of scheduling and assignment problems. In this paper we review several variants of graph coloring, such as precoloring extension, list coloring, multicoloring, minimum sum coloring, and discuss their applications in scheduling.