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Scheduling Split Intervals
, 2002
"... We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Mo ..."
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Cited by 57 (5 self)
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We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job Jj is associated with an interval, Ij, which consists of up to t segments, for some t _) 1, a of their segments intersect. Such jobs show up in a I.I Problem Statement and Motivation. We wide range of applications, including the transmission consider the problem of scheduling jobs that are given of continuousmedia data, allocation of linear resources as groups of nonintersecting segments on the real line. (e.g. bandwidth in linear processor arrays), and in Each job Jj is associated with a tinterval, Ij, which
Spike: Intelligent scheduling of hubble space telescope observations
 Intelligent Scheduling
, 1994
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Identical coupled task scheduling: polynomial complexity of the cyclic case. Cahiers Leibniz 179
, 2009
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Identical coupled task scheduling problem: the finite case
, 2011
"... Abstract: Coupled tasks belong to the class of multioperation tasks, where two consecutive operations are separated by a certain time interval of fixed duration. The objective is to schedule the tasks on one machine in order to minimize the makespan. Such problems occur especially in the case of th ..."
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Cited by 1 (1 self)
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Abstract: Coupled tasks belong to the class of multioperation tasks, where two consecutive operations are separated by a certain time interval of fixed duration. The objective is to schedule the tasks on one machine in order to minimize the makespan. Such problems occur especially in the case of the management of radar systems. The complexity status of this problem has been settled for all particular cases, except the case of the identical coupled task problem, where one has multiple copies of a single coupled task. This scheduling problem seems to be simple at first glance. However, its complexity status (for both, the cyclic and the finite case) has remained open for many years. Recently, Vassilissa LehouxLebacque, Gerd Finke and Nadia Brauner proved that the cyclic case is polynomial. The aim of this work was to study the finite case by using some of the results and structures known from the cyclic case. We have been able to see that the finite case strongly differs from the cyclic case. Using integer programming and the commercial solver CPLEX, we have obtained a series of optimal solutions for small instances. The structures underlying these solutions are much more complicated than those of the cyclic case. Eventually, we have obtained results that let us think that this problem is not in NP.
A Note on Scheduling Identical Coupled Tasks in Constant Time Philippe
"... The coupled tasks problem consists in scheduling n jobs on a single machine. Each job i is made of two operations with processing times ai and bi and a fixed required delay Li between them. Operations cannot overlap in time but operations of different jobs can be interleaved. The objective is to min ..."
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The coupled tasks problem consists in scheduling n jobs on a single machine. Each job i is made of two operations with processing times ai and bi and a fixed required delay Li between them. Operations cannot overlap in time but operations of different jobs can be interleaved. The objective is to minimize the makespan of the schedule. In this note we show that the problem with identical jobs (∀i, ai = a, bi = b, Li = L) can be solved in constant time when a, b, L are fixed. This problem is motivated by radar scheduling applications where tasks corresponding to transmitting radiowaves and listening to potential echoes are coupled.
Coupledtasks in presence of bipartite compatibilities graphs
"... Abstract. We tackle the makespan minimization coupledtasks problem in presence of incompatibility constraints. In particular, we focus on stretched coupledtasks, i.e.coupledtasks having the same subtasks execution time and idle time duration. We study several problems in the framework of classi ..."
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Abstract. We tackle the makespan minimization coupledtasks problem in presence of incompatibility constraints. In particular, we focus on stretched coupledtasks, i.e.coupledtasks having the same subtasks execution time and idle time duration. We study several problems in the framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain,...). In such context, we design efficient polynomialtime approximation algorithms according to different parameters of the scheduling problem. 1
Scheduling coupledtasks with incompatibility constraint: a binpacking related problem
"... Abstract. We tackle the makespan minimization problem of coupledtasks in presence of compatibility constraint. In particular, we focus on stretched coupledtasks, i.e. coupledtasks having the same subtasks execution time and idle time duration. We show the relationship with bin packing problems f ..."
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Abstract. We tackle the makespan minimization problem of coupledtasks in presence of compatibility constraint. In particular, we focus on stretched coupledtasks, i.e. coupledtasks having the same subtasks execution time and idle time duration. We show the relationship with bin packing problems for some configurations, and study several problems in framework of complexity and approximation for which the topology of the compatibility graph is specific (star, chain, bipartite,...). 1
(2009)" Complexity and approximation for scheduling problem for a torpedo
"... This paper considers a special case of the coupledtasks scheduling problem on one processor. The general problems were analyzed in depth by Orman and Potts [1]. In this paper, we consider that all processing times are equal to 1, the gap has exact length L, we have precedence constraints, compatibi ..."
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This paper considers a special case of the coupledtasks scheduling problem on one processor. The general problems were analyzed in depth by Orman and Potts [1]. In this paper, we consider that all processing times are equal to 1, the gap has exact length L, we have precedence constraints, compatibility constraints are introduced and the criterion is to minimize the scheduling length. We use this problem to study the problem of data acquisition and data treatment of a torpedo under the water. We show that this problem is N Pcomplete and we propose an ρapproximation algorithm where ρ ≤ (L+6) 6
de systèmes complexes
"... Rapport de recherche n ° 4602 — Octobre 2002 — 12 pages Abstract: We consider a system made of one resource. The execution of the tasks is nonpreemptive on this resource. The tasks we consider are composed of a given number of subtasks, two consecutives subtasks being separated by an idle period. T ..."
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Rapport de recherche n ° 4602 — Octobre 2002 — 12 pages Abstract: We consider a system made of one resource. The execution of the tasks is nonpreemptive on this resource. The tasks we consider are composed of a given number of subtasks, two consecutives subtasks being separated by an idle period. These idle periods may be used for executing other subtasks. We wish to insert a new task in a given schedule. The characteristics of this task are not known before it appears, and its execution must be completed before a given deadline. The criterion is the minimization of the increase of the sum of the delays of the tasks.