Machine Speed Scaling by Adapting Methods for Convex Optimization with Submodular Constraints

Shioura, Akiyoshi; Shakhlevich, Natalia V.; Strusevich, Vitaly A.

doi:10.1287/ijoc.2017.0758

Cited by 9 publications

(9 citation statements)

References 38 publications

(37 reference statements)

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“…[127] extends this result to a range of different strictly convex cost functions for the case of continuous variables. Their result is used in [128] to solve optimization problems on graphs and in [153] to derive efficient algorithms for processor scheduling problems. For a special case of RAPs with nested constraints, the equivalence of (a, b, f )-separable RAPs is proven in [5] for the case where the functions f are strictly convex and differentiable, b = 0, and where the variables are continuous.…”

Section: Reduction Results In the Literaturementioning

confidence: 99%

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Duality-driven optimization in energy management: offline and online algorithms for resource allocation problems

Uiterkamp

Hendrik²

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Section: Reduction Results In the Literaturementioning

confidence: 99%

“…Recently, [153] applied the equivalence result in [127] to improve the time complexity of several other speed scaling problems. Together with the result in this section, this suggests that there is a great potential for using the reduction result in this chapter to contribute to more efficient algorithms within this research field.…”

Section: 55mentioning

confidence: 99%

Duality-driven optimization in energy management: offline and online algorithms for resource allocation problems

Uiterkamp

Hendrik²

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“…5. In our recent paper Shioura, Shakhlevich and Strusevich (2017) , we demonstrate how the flow and submodular optimization techniques can be applied to the off-line problems of speed scaling. These problems reduce to minimizing convex separable functions under submodular constraints.…”

Section: Discussionmentioning

confidence: 99%

Preemptive models of scheduling with controllable processing times and of scheduling with imprecise computation: A review of solution approaches

Shioura

Shakhlevich

Strusevich

2018

European Journal of Operational Research

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a b s t r a c tThis paper provides a review of recent results on scheduling with controllable processing times. The stress is on the methodological aspects that include parametric flow techniques and methods for solving mathematical programming problems with submodular constraints. We show that the use of these methodologies yields fast algorithms for solving problems on single machine or parallel machines, with either one or several objective functions. For a wide range of problems with controllable processing times we report algorithms with the running times which match those known for the corresponding problems with fixed processing times. As a by-product, we present the best possible algorithms for a number of problems on parallel machines that are traditionally studied within the body of research on scheduling with imprecise computation.

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“…Recently, Shioura et al (2017) applied the equivalence result in Nagano and Aihara (2012) to improve the time complexity of several other speed-scaling problems. Together with the result in this section, this suggests that there is a great potential for using the reduction result in this article to contribute to more efficient algorithms within this research field.…”

Section: Storage Operation In Energy Systemsmentioning

confidence: 99%

“…Nagano and Aihara (2012) extend this result to a range of different strictly convex cost functions for the case of continuous variables. Their result is used by Nagano and Kawahara (2013) to solve optimization problems on graphs and by Shioura et al (2017) to derive efficient algorithms for processor scheduling problems. For a special case of RAPs with nested constraints, the equivalence of (a, b, f )-separable RAPs is proven by Akhil and Sundaresan (2018) for the case in which the functions f are strictly convex and differentiable, b 0, and with continuous variables.…”

Section: Introductionmentioning

confidence: 99%

On a Reduction for a Class of Resource Allocation Problems

Uiterkamp

Gerards

Hurink

2022

INFORMS Journal on Computing

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In the resource allocation problem (RAP), the goal is to divide a given amount of a resource over a set of activities while minimizing the cost of this allocation and possibly satisfying constraints on allocations to subsets of the activities. Most solution approaches for the RAP and its extensions allow each activity to have its own cost function. However, in many applications, often the structure of the objective function is the same for each activity, and the difference between the cost functions lies in different parameter choices, such as, for example, the multiplicative factors. In this article, we introduce a new class of objective functions that captures a significant number of the objectives occurring in studied applications. These objectives are characterized by a shared structure of the cost function depending on two input parameters. We show that, given the two input parameters, there exists a solution to the RAP that is optimal for any choice of the shared structure. As a consequence, this problem reduces to the quadratic RAP, making available the vast amount of solution approaches and algorithms for the latter problem. We show the impact of our reduction result on several applications, and in particular, we improve the best-known worst-case complexity bound of two problems in vessel routing and processor scheduling from [Formula: see text] to [Formula: see text]. Summary of Contribution: The resource allocation problem (RAP) with submodular constraints and its special cases are classic problems in operations research. Because these problems are studied in many different scientific disciplines, many conceptual insights, structural properties, and solution approaches have been reinvented and rediscovered many times. The goal of this article is to reduce the amount of future reinventions and rediscoveries by bringing together these different perspectives on RAPs in a way that is accessible to researchers with different backgrounds. The article serves as an exposition on RAPs and on their wide applicability in many areas, including telecommunications, energy, and logistics. In particular, we provide tools and examples that can be used to formulate and solve problems in these areas as RAPs. To accomplish this, we make three concrete contributions. First, we provide a survey on algorithms and complexity results for RAPs and discuss several recent advances in these areas. Second, we show that many objectives for RAPs can be reduced to a (simpler) quadratic objective function, which makes available the extensive collection of fast and efficient algorithms for quadratic RAPs to solve these problems. Third, we discuss the impact that RAPs and the aforementioned reduction result can make in several application areas.

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Machine Speed Scaling by Adapting Methods for Convex Optimization with Submodular Constraints

Cited by 9 publications

References 38 publications

Duality-driven optimization in energy management: offline and online algorithms for resource allocation problems

Duality-driven optimization in energy management: offline and online algorithms for resource allocation problems

Preemptive models of scheduling with controllable processing times and of scheduling with imprecise computation: A review of solution approaches

On a Reduction for a Class of Resource Allocation Problems

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