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A formal analysis and taxonomy of task allocation in multirobot systems
 INT’L. J. OF ROBOTICS RESEARCH
, 2004
"... Despite more than a decade of experimental work in multirobot systems, important theoretical aspects of multirobot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multirobot task allocation (MRTA). Most work on MRTA has been ad hoc ..."
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Cited by 213 (4 self)
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Despite more than a decade of experimental work in multirobot systems, important theoretical aspects of multirobot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multirobot task allocation (MRTA). Most work on MRTA has been ad hoc and empirical, with many coordination architectures having been proposed and validated in a proofofconcept fashion, but infrequently analyzed. With the goal of bringing objective grounding to this important area of research, we present a formal study of MRTA problems. A domainindependent taxonomy of MRTA problems is given, and it is shown how many such problems can be viewed as instances of other, wellstudied, optimization problems. We demonstrate how relevant theory from operations research and combinatorial optimization can be used for analysis and greater understanding of existing approaches to task allocation, and to show how the same theory can be used in the synthesis of new approaches.
List Scheduling with and without Communication Delays
 Parallel Computing
, 1993
"... Empirical results have shown that the classical critical path (CP) list scheduling heuristic for task graphs is a fast and practical heuristic when communication cost is zero. In the first part of this paper we study the theoretical properties of the CP heuristic that lead to near optimum performanc ..."
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Cited by 38 (6 self)
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Empirical results have shown that the classical critical path (CP) list scheduling heuristic for task graphs is a fast and practical heuristic when communication cost is zero. In the first part of this paper we study the theoretical properties of the CP heuristic that lead to near optimum performance in practice. In the second part we extend the CP analysis to the problem of ordering the task execution when the processor assignment is given and communication cost is nonzero. We propose two new list scheduling heuristics, the RCP and RCP 3 that use critical path information and ready list priority scheduling. We show that the performance properties for RCP and RCP 3 , when communication is nonzero, are similar to CP when communication is zero. Finally, we present an extensive experimental study and optimality analysis of the heuristics which verifies our theoretical results. 1 Introduction The processor scheduling problem is of considerable importance in parallel processing. Given a...
A Formal Framework For The Study Of Task Allocation In MultiRobot Systems
, 2003
"... Despite more than a decade of experimental work in multirobot systems, important theoretical aspects of multirobot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multirobot task allocation (MRTA). Most work on MRTA has been ad hoc ..."
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Cited by 27 (6 self)
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Despite more than a decade of experimental work in multirobot systems, important theoretical aspects of multirobot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multirobot task allocation (MRTA). Most work on MRTA has been ad hoc and empirical, with many coordination architectures having been proposed and validated in a proofofconcept fashion, but infrequently analyzed. With the goal of bringing objective grounding to this important area of research, we present a formal study of MRTA problems. A domainindependent taxonomy of MRTA problems is given, and it is shown how many such problems can be viewed as instances of other, wellstudied, optimization problems. We demonstrate how relevant theory from operations research and combinatorial optimization can be used for analysis and greater understanding of existing approaches to task allocation, and show how the same theory can be used in the synthesis of new approaches.
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 25 (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...
The Complexity of Path Coloring and Call Scheduling
 Theoretical Computer Science
, 2000
"... Modern highperformance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests. In alloptical networks with wavelengthdivision multiplexing, connection requests must be assigned paths and colors (wavelengths) such that i ..."
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Cited by 24 (7 self)
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Modern highperformance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests. In alloptical networks with wavelengthdivision multiplexing, connection requests must be assigned paths and colors (wavelengths) such that intersecting paths receive different colors, and the goal is to minimize the number of colors used. This path coloring problem is proved NPhard for undirected and bidirected ring networks. Path coloring in undirected tree networks is shown to be equivalent to edge coloring of multigraphs, which implies a polynomialtime optimal algorithm for trees of constant degree as well as NPhardness and an approximation algorithm with absolute approximation ratio 4:3 and asymptotic approximation ratio 1:1 for trees of arbitrary degree. For bidirected trees, path coloring is shown to be NPhard even in the binary case. A polynomialtime optimal algorithm is given for path coloring in undirected or bidir...
Selected problems of scheduling tasks in multiprocessor computing systems
 PHD THESIS, INSTYTUT INFORMATYKI POLITECHNIKA POZNANSKA
, 1997
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A Polynomial Time Approximation Scheme For General Multiprocessor Job Scheduling
 In STOC
, 1999
"... . Recently, there have been considerable interests in the multiprocessor job scheduling problem, in which a job can be processed in parallel on one of several alternative subsets of processors. In this paper, a polynomial time approximation scheme is presented for the problem in which the number of ..."
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Cited by 19 (2 self)
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. Recently, there have been considerable interests in the multiprocessor job scheduling problem, in which a job can be processed in parallel on one of several alternative subsets of processors. In this paper, a polynomial time approximation scheme is presented for the problem in which the number of processors in the system is a fixed constant. This result is the best possible because of the strong NPhardness of the problem, and is a significant improvement over the past results: the best previous result was an approximation algorithm of ratio 7=6 + ffl for 3processor systems, based on Goemans' algorithm for a restricted version of the problem. Key words. job scheduling, approximation algorithm, polynomial time approximation scheme, multiprocessor processing AMS subject classifications. 68Q20, 68Q25, 90B35, 90C27, 90C39 1. Introduction. One of the assumption made in classical scheduling theory is that a job is always executed by one processor at a time. With the advances in paralle...
Scheduling to Minimize the Average Completion Time of Dedicated Tasks
, 2000
"... We propose a polynomial time approximation scheme for scheduling a set of dedicated tasks on a constant number m of processors in order to minimize the sum of completion times Pmjx j j P C j . In addition we give a polynomial time approximation scheme for the weighted preemptive problem with ..."
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Cited by 16 (3 self)
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We propose a polynomial time approximation scheme for scheduling a set of dedicated tasks on a constant number m of processors in order to minimize the sum of completion times Pmjx j j P C j . In addition we give a polynomial time approximation scheme for the weighted preemptive problem with release dates, Pmjx j ; pmtn; r j j P w j C j . 1 Introduction In this paper we consider the problem of scheduling dedicated tasks on a set of processors in order to minimize the sum of task completion times. Using the This research was partially supported by the ASP \Approximabilite et Recherche Locale" of the French Ministry of Education, Research and Technology (MENRT), by the DFG  Graduiertenkolleg \Eziente Algorithmen und Mehrskalenmethoden" and by the EU project APPOL, \Approximation and online algorithms", IST199914084. y National Technical University of Athens, Heroon Polytechniou 9, 15773, Athens, Greece, afrati@softlab.ece.ntua.gr z LaMI, Universite d'Evry, Boul...
General multiprocessor task scheduling
, 1999
"... Abstract: Most papers in the scheduling field assume that a job can be processed by only one machine at a time. Namely, they use a onejobononemachine model. In many industry settings, this may not be an adequate model. Motivated by human resource planning, diagnosable microprocessor systems, ber ..."
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Cited by 15 (5 self)
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Abstract: Most papers in the scheduling field assume that a job can be processed by only one machine at a time. Namely, they use a onejobononemachine model. In many industry settings, this may not be an adequate model. Motivated by human resource planning, diagnosable microprocessor systems, berth allocation, and manufacturing systems that may require several resources simultaneously to process a job, we study the problem with a onejobonmultiplemachine model. In our model, there are several alternatives that can be used to process a job. In each alternative, several machines need to process simultaneously the job assigned. Our purpose is to select an alternative for each job and then to schedule jobs to minimize the completion time of all jobs. In this paper, we provide a pseudopolynomial algorithm to solve optimally the twomachine problem, and a combination of a fully polynomial scheme and a heuristic to solve the threemachine problem. We then extend the results to a general mmachine problem. Our algorithms also provide an effective lower bounding scheme which lays the foundation for solving optimally the general mmachine problem. Furthermore, our algorithms can also be applied to solve a special case of the threemachine problem in pseudopolynomial time. Both pseudopolynomial algorithms (for twomachine and threemachine problems) are much more
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...