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Optimal and Online Preemptive Scheduling on Uniformly Related Machines
"... We consider the problem of preemptive scheduling on uniformly related machines. We present a semionline algorithm which, if the optimal makespan is given in advance, produces an optimal schedule. Using the standard ..."
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We consider the problem of preemptive scheduling on uniformly related machines. We present a semionline algorithm which, if the optimal makespan is given in advance, produces an optimal schedule. Using the standard
Approximation schemes for packing with item fragmentation. Theory Comput
 Syst
"... We consider two variants of the classical bin packing problem in which items may be fragmented. This can potentially reduce the total number of bins needed for packing the instance. However, since fragmentation incurs overhead, we attempt to avoid it as much as possible. In bin packing with size inc ..."
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We consider two variants of the classical bin packing problem in which items may be fragmented. This can potentially reduce the total number of bins needed for packing the instance. However, since fragmentation incurs overhead, we attempt to avoid it as much as possible. In bin packing with size increasing fragmentation (BPSIF), fragmenting an item increases the input size (due to a header/footer of fixed size that is added to each fragment). In bin packing with size preserving fragmentation (BPSPF), there is a bound on the total number of fragmented items. These two variants of bin packing capture many practical scenarios, including message transmission in community TV networks, VLSI circuit design and preemptive scheduling on parallel machines with setup times/setup costs. While both BPSPF and BPSIF do not belong to the class of problems that admit a polynomial time approximation scheme (PTAS), we show in this paper that both problems admit a dual PTAS and an asymptotic PTAS. We also develop for each of the problems a dual asymptotic fully polynomial time approximation scheme (AFPTAS). Our AFPTASs are based on a nonstandard transformation of the mixed packing and covering linear program formulations of our problems into pure covering programs, which enables to efficiently solve these programs.
Robust Algorithms for Preemptive Scheduling
 ALGORITHMICA
, 2012
"... Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to run on a set of m machines. A job can be sp ..."
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Cited by 3 (0 self)
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Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to run on a set of m machines. A job can be split into parts arbitrarily and these parts are to be assigned to time slots on the machines without parallelism, that is, for every job, at most one of its parts can be processed at each time. Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms for constructing preemptive schedules. Robust algorithms receive one piece of input at a time. They may change a small portion of the solution as an additional part of the input is revealed. The capacity of change is based on the size of the new piece of input. For scheduling problems, the supremum ratio between the total size of the jobs (or parts of jobs) which may be rescheduled upon the arrival of a new job j, and the size of j, is called migration factor. We design a strongly optimal algorithm with the migration factor 1 − 1 m for identical machines. Strongly optimal algorithms avoid idle time and create solutions where the (nonincreasingly) sorted vector of completion times of the machines is lexicographically minimal. In the case of identical machines this results not only in makespan minimization, but the created solution is also optimal with respect to any ℓp norm (for p>1). We show that an algorithm of a smaller migration factor cannot be optimal with respect to makespan or any other ℓp norm, thus the result is best possible in this sense as well. We further show that neither uniformly related machines
Optimal preemptive scheduling for general target functions
 Journal of Computer and System Sciences
"... We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and m ≤ n uniformly related machines, one aims at scheduling the jobs to the machines, allowing preemptions but forbidding parallelization, so that a given target fun ..."
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We study the problem of optimal preemptive scheduling with respect to a general target function. Given n jobs with associated weights and m ≤ n uniformly related machines, one aims at scheduling the jobs to the machines, allowing preemptions but forbidding parallelization, so that a given target function of the loads on each machine is minimized. This problem was studied in the past in the case of the makespan. Gonzalez and Sahni [6] and later Shachnai, Tamir and Woeginger [12] devised a polynomial algorithm that outputs an optimal schedule for which the number of preemptions is at most 2(m − 1). We extend their ideas for general symmetric, convex and monotone target functions. This general approach enables us to distill the underlying principles on which the optimal makespan algorithm is based. More specifically, the general approach enables us to identify between the optimal scheduling problem and a corresponding problem of mathematical programming. This, in turn, allows us to devise a single algorithm that is suitable for a wide array of target functions, where the only difference between one target function and another is manifested through the corresponding mathematical programming problem.
Optimal and online preemptive scheduling on uniformly related machines
, 2007
"... We consider the problem of preemptive scheduling on uniformly related machines. We present a semionline algorithm which, if the optimal makespan is given in advance, produces an optimal schedule. Using the standard doubling technique, this yields a 4competitive deterministic and an e ≈ 2.71compet ..."
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We consider the problem of preemptive scheduling on uniformly related machines. We present a semionline algorithm which, if the optimal makespan is given in advance, produces an optimal schedule. Using the standard doubling technique, this yields a 4competitive deterministic and an e ≈ 2.71competitive randomized online algorithm. In addition, it matches the performance of the previously known algorithms for the offline case, with a considerably simpler proof. Finally, we study the performance of greedy heuristics for the same problem.
Preemptive scheduling on selfish machines
"... Abstract. We consider the problem of scheduling on parallel uniformly related machines, where preemptions are allowed and the machines are controlled by selfish agents. Our goal is to minimize the makespan, whereas the goal of the agents is to maximize their profit. We show that a known algorithm is ..."
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Abstract. We consider the problem of scheduling on parallel uniformly related machines, where preemptions are allowed and the machines are controlled by selfish agents. Our goal is to minimize the makespan, whereas the goal of the agents is to maximize their profit. We show that a known algorithm is monotone and can therefore be used to create a truthful mechanism for this problem which achieves the optimal makespan. We extend this result for additional common goal functions. 1
RequestInitiated Resource Contention • InterdomainInitiated Resource Contention • OriginInitiated Resource Contention
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Dynamic Windows Scheduling with Reallocation?
"... Abstract. We consider the Windows Scheduling problem. The problem is a restricted version of UnitFractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels to clients. Each client ci i ..."
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Abstract. We consider the Windows Scheduling problem. The problem is a restricted version of UnitFractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels to clients. Each client ci is characterized by an active cycle and a window wi. During the period of time that any given client ci is active, there must be at least one transmission from ci scheduled in any wi consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the number of channels used. We extend previous online models, where decisions are permanent, assuming that clients may be reallocated at some cost. We assume that such cost is a constant amount paid per reallocation. That is, we aim to minimize also the number of reallocations. We present three online reallocation algorithms for Windows Scheduling. We evaluate experimentally these protocols showing that, in practice, all three achieve constant amortized reallocations with close to optimal channel usage. Our simulations also expose interesting tradeoffs between reallocations and channel usage. We introduce a new objective function for WS with reallocations, that can be also applied to models where reallocations are not possible. We analyze this metric for one of the algorithms which, to the best of our knowledge, is the first online WS protocol with theoretical guarantees that applies to scenarios where clients may leave and the analysis is against current load rather than peak load. Using previous results, we also observe bounds on channel usage for one of the algorithms.
Article in Lecture Notes in Computer Science · January 2009 Impact Factor: 0.51 · Source: DBLP CITATIONS
"... Optimal and online preemptive scheduling on uniformly related machines ..."