We study online scheduling on two unbounded parallel-batching machines with limited restarts to minimize the makespan. In this system jobs arrive over time and a batch can be restarted if and only if all the jobs in i...
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We study online scheduling on two unbounded parallel-batching machines with limited restarts to minimize the makespan. In this system jobs arrive over time and a batch can be restarted if and only if all the jobs in it have never been restarted. To tackle this difficult problem, we make the second-restart assumption whereby we can only interrupt a running batch B at time t if both machines are busy at time t and batch B has a later starting time than the other running batch. For this case, we provide a best online algorithm with a competitive ratio root 3+1/2 approximate to 1.366. For the general problem, we show that no online algorithms can have a competitive ratio less than 1.298, leaving a gap from 1.298 to 1.366. (C) 2010 Elsevier B.V. All rights reserved.
This paper investigates two different semi-online versions of the machine covering, which is the problem of assigning a set of jobs to a system of m(m >= 3) identical parallel machines so as to maximize the earlies...
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This paper investigates two different semi-online versions of the machine covering, which is the problem of assigning a set of jobs to a system of m(m >= 3) identical parallel machines so as to maximize the earliest machine completion time. In the first case, we assume that the largest processing times is known in advance. In the second case, we assume that the total processing times of all jobs is known in advance. For each version we propose a semi-online algorithm and investigate its competitive ratio. The competitive ratio of each algorithm is 1/m-1, which is shown to be the best possible competitive ratio for each semi-online problem.
In this paper, a new algorithm for constructing the relative neighborhood graph(RNG) of an n points set in Euclidean k-dimensional space is presented, for fixed k greater-than-or-equal-to 3. The worst case running tim...
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In this paper, a new algorithm for constructing the relative neighborhood graph(RNG) of an n points set in Euclidean k-dimensional space is presented, for fixed k greater-than-or-equal-to 3. The worst case running time of the algorithm is O(n2-a(k)(log n)1-a(k)), for a(k) = 2-(k+1), which is under the assumption that no three input points form an isosceles triangle. Previous algorithms need O(n2) time. Our algorithm proceeds in two phases. First, a supergraph of RNG with O(n) edges is constructed and then those edges which do not belong to RNG are eliminated.
Nowadays, it is popular that the dealer makes profits by selling a kind of discount coupons, which can be used as money to purchase commodities with total cost less than or equal to the face value of the coupon. We ca...
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Nowadays, it is popular that the dealer makes profits by selling a kind of discount coupons, which can be used as money to purchase commodities with total cost less than or equal to the face value of the coupon. We can purchase a coupon at a price of 0 < s <= 1 times its face value and the number of potential purchasable coupons is a given integer l. The customer has the option to buy the goods by cash completely or by a discount coupon. However, each piece of goods can only use one coupon and the coupon used must have enough balance for the goods. The objective is to minimize the total cost for purchasing all the goods. In this paper, we reduce the problem to a special bin packing model. We consider the online problems for all 0 < s <= 1 and 1 <= t <= infinity. We present optimal online algorithms for all 0 < s <= 1 when l = infinity and l = 1. For 2 <= l < infinity, we give both a lower bound and an algorithm, and show the algorithm is optimal for l = 2.
Reliability-based weight optimization of a generic, fighter-like wing structure is conducted for gust response and aileron effectiveness constraints. The formulation accounts for parametric uncertainties in these aero...
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Reliability-based weight optimization of a generic, fighter-like wing structure is conducted for gust response and aileron effectiveness constraints. The formulation accounts for parametric uncertainties in these aeroelastic response quantities. Reliability indices measure the probability of satisfying each constraint, and a preliminary design procedure is developed in which constraints are enforced on these indices. This framework integrates ASTROS for structural and loads analysis, object-oriented MATLAB(R) tools for reliability analysis, and DOT for optimization and most probable point estimation. The reliability analysisalgorithm takes advantage of adaptive nonlinear approximations to compensate for nonlinearity of the failure surfaces. The wing structure is modeled with finite elements, each of which is assumed to have random thickness of known standard deviation. Young's modulus of the wing skin material is also assumed to be random. Mean thickness values are taken as design variables. Linear unsteady aerodynamics is used to estimate frequency response functions caused by continuous gust loads. Reliability index constraints are-enforced for gust-induced bending moment and shear at the wing's root, and also for aileron effectiveness. Redistribution of structural mass by the optimizer produces designs with improved aeroelastic performance reliability and relatively small weight penalties.
This paper considers on-line and semi-on-line scheduling problems on m parallel machines with objective to maximize the minimum load. For on-line version, we prove that algorithm Random is an optimal randomized algori...
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This paper considers on-line and semi-on-line scheduling problems on m parallel machines with objective to maximize the minimum load. For on-line version, we prove that algorithm Random is an optimal randomized algorithm on two machines, and derive a new randomized upper bound for general m machines which significantly improves the known upper bound. For semi-on-line version with non-increasing job processing times, we show that LS algorithm is an optimal deterministic algorithm for two and three machine cases. We further present an optimal randomized algorithm RLS for two machine case.
This paper investigates two different semi on-line scheduling problems on a two-machine system. In the first case, we assume that all jobs have their processing times in between p and rp (p > 0, r greater than or e...
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This paper investigates two different semi on-line scheduling problems on a two-machine system. In the first case, we assume that all jobs have their processing times in between p and rp (p > 0, r greater than or equal to 1). In the second case, we assume that the largest processing time is known in advance. We show that one has a best possible algorithm with worst case ratio 4/3 while LS is still the best possible for the other problem with ratio (r + 1)/2 which is still 3/2 in the worst case r = 2.
In (Hui and Martel, 1993), we designed and analyzed efficient self-adjusting linear list algorithms. Our analysis proves that a self-adjusting linear list algorithm, MP, is competitive to a large class of offline adve...
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In (Hui and Martel, 1993), we designed and analyzed efficient self-adjusting linear list algorithms. Our analysis proves that a self-adjusting linear list algorithm, MP, is competitive to a large class of offline adversaries, where the operations are successful searches, unsuccessful searches, and insertions. analysis of deletions is listed as an open question. This paper presents an improved version of MP which is also able to handle deletions efficiently, and proves that the new MP algorithm is 6-competitive to offline adversaries when considering successful searches, unsuccessful searches, insertions, and deletions.
In this monograph we survey results from a newly emerging line of research that targets algorithmanalysis in the physical interference model. In the main part of our monograph we focus on wireless scheduling: given a...
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In this monograph we survey results from a newly emerging line of research that targets algorithmanalysis in the physical interference model. In the main part of our monograph we focus on wireless scheduling: given a set of communication requests, arbitrarily distributed in space, how can these requests be scheduled efficiently? We study the difficulty of this problem and we examine algorithms for wireless scheduling with provable performance guarantees. Moreover, we present a few results for related problems and give additional context.
This paper investigates on-line parallel machine scheduling problems. We show the optimality of the classical LS algorithm. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper investigates on-line parallel machine scheduling problems. We show the optimality of the classical LS algorithm. (C) 2000 Elsevier Science Ltd. All rights reserved.
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