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58
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 46 (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.
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 26 (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...
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 25 (5 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.
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 18 (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 (5 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...
Improved Bounds for Scheduling Conflicting Jobs with Minsum Criteria
"... We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among the jobs are formed as an arbitrary conflict graph. Building on ..."
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Cited by 7 (2 self)
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We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among the jobs are formed as an arbitrary conflict graph. Building on the framework of Queyranne and Sviridenko (J. of Scheduling, 5:287305, 2002), we present a general technique for reducing the weighted sum of completion times problem to the classical makespan minimization problem. Using this technique, we improve the best known results for scheduling conflicting jobs with minsum objective, on several fundamental classes of graphs, including line graphs, (k +1)claw free graphs and perfect graphs. In particular, we obtain the first constant factor approximation ratio for nonpreemptive scheduling on interval graphs. We also improve the results of Kim (SODA 2003, 97–98) for scheduling jobs on line graphs and for resourceconstrained scheduling.
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.
A Lower Bound For OnLine File Transfer Routing And Scheduling
 IN PROCEEDINGS OF THE 1997 CONFERENCE ON INFORMATION SCIENCES AND SYSTEMS
, 1997
"... In this paper, we study the OnLine File Transfer Routing and Scheduling problem. Given a sequence of file transfer requests and a graph that represents a network, the problem is to determine both a route and schedule for each file transfer in the sequence so as to minimize a suitable objective func ..."
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Cited by 7 (1 self)
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In this paper, we study the OnLine File Transfer Routing and Scheduling problem. Given a sequence of file transfer requests and a graph that represents a network, the problem is to determine both a route and schedule for each file transfer in the sequence so as to minimize a suitable objective function. We require that an algorithm be online in the sense that it must respond to each request in the order given and before future requests are known. We show that there is no online algorithm which produces solutions with network congestion smaller than blog kc + 1 times that of the optimal solution or makespan smaller than blog kc 2 + 1 times that of the optimal solution, where k is the number of file transfer requests. We explain that this bound also holds for randomized online algorithms versus an adaptive online adversary. We discuss briefly the performance of several greedy online algorithms both theoretically and in practice.