Smart-Grid Electricity Allocation via Strip Packing with Slicing

Alamdari, Soroush; Biedl, Thérèse; Chan, Timothy M.; Grant, Elyot; Jampani, Krishnam Raju; Keshav, Srinivasan; Lubiw, Anna; Pathak, Vinayak

doi:10.1007/978-3-642-40104-6_3

Cited by 18 publications

(13 citation statements)

References 19 publications

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“…Alamdari et al [3] explored algorithms for a variant of 2SP where items can be sliced using vertical cuts, which has applications in smart-grid electricity allocation. Many packing algorithms [28,23,8] solve the sliceable version of the problem as a subroutine.…”

Section: Preliminariesmentioning

confidence: 99%

Tight Approximation Algorithms for Geometric Bin Packing with Skewed Items

Khan¹,

Sharma²

2021

Preprint

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In the Two-dimensional Bin Packing (2BP) problem, we are given a set of rectangles of height and width at most one and our goal is to find an axis-aligned nonoverlapping packing of these rectangles into the minimum number of unit square bins. The problem admits no APTAS and the current best approximation ratio is 1.406 by Bansal and Khan [SODA'14]. A well-studied variant of the problem is Guillotine Two-dimensional Bin Packing (G2BP), where all rectangles must be packed in such a way that every rectangle in the packing can be obtained by recursively applying a sequence of end-to-end axis-parallel cuts, also called guillotine cuts. Bansal, Lodi, and Sviridenko [FOCS'05] obtained an APTAS for this problem. Let λ be the smallest constant such that for every set I of items, the number of bins in the optimal solution to G2BP for I is upper bounded by λ opt(I) + c, where opt(I) is the number of bins in the optimal solution to 2BP for I and c is a constant. It is known that 4/3 ≤ λ ≤ 1.692. Bansal and Khan [SODA'14] conjectured that λ = 4/3. The conjecture, if true, will imply a (4/3+ε)-approximation algorithm for 2BP. According to convention, for a given constant δ > 0, a rectangle is large if both its height and width are at least δ, and otherwise it is called skewed. We make progress towards the conjecture by showing λ = 4/3 for skewed instance, i.e., when all input rectangles are skewed. Even for this case, the previous best upper bound on λ was roughly 1.692. We also give an APTAS for 2BP for skewed instance, though general 2BP does not admit an APTAS.

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Section: Preliminariesmentioning

confidence: 99%

Tight Approximation Algorithms for Geometric Bin Packing with Skewed Items

Khan¹,

Sharma²

2021

Preprint

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“…Observation 18. For any job J and its nice job J * transformed by Convert, (i) I(J) ⊆ I(J * ); (ii) I(J) = I(J * ) if and only if |I(J)| < 2 p ; in this case, den(J) > 1 2 and den(J * ) = 1. We then define two procedures that transform schedules related to nice job sets.…”

Section: Nice Job Set and Transformationsmentioning

confidence: 99%

“…The main combinatorial problem we defined in this paper has analogy to the traditional load balancing problem [3] and machine minimization problem [9,12,13,42] but the main differences are the objective being maximum load and jobs are unit height [9,12,13,42]. Minimizing maximum load has also been looked at in the context of smart grid [1,26,45,50,51], some of which further consider allowing reshaping of the jobs [1,26]. As to be discussed in Section 2, our problem is more difficult than minimizing the maximum load.…”

Section: Introductionmentioning

confidence: 99%

Non-preemptive Scheduling in a Smart Grid Model and its Implications on Machine Minimization

Liu¹,

Liu²,

Wong³

2016

Preprint

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We study a scheduling problem arising in demand response management in smart grid. Consumers send in power requests with a flexible feasible time interval during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. Previous work has studied cases where jobs have unit power requirement and unit duration. We extend the study to arbitrary power requirement and duration, which has been shown to be NP-hard. We give the first online algorithm for the general problem, and prove that the problem is fixed parameter tractable. We also show that the online algorithm is asymptotically optimal when the objective is to minimize the peak load. In addition, we observe that the classical non-preemptive machine minimization problem is a special case of the smart grid problem with min-peak objective, and show that we can solve the non-preemptive machine minimization problem asymptotically optimally.

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“…Since this peak demand occurs in relatively short fraction of the entire year, much of the capacity is not utilized for large parts of the year. In 2009, for example, 15% of the generation capacity in Massachusetts was utilized less than 88 hours [1], [2] or 1% of the year. Therefore, it is desirable to reduce the peak power demand as it has a direct impact on the need to invest in expensive infrastructure.…”

Section: Introductionmentioning

confidence: 99%

“…al. [1] propose a fully polynomial time approximation scheme for preemptive OCOSP, but since they use the ellipsoid method in their linear program of FPTAS, it is not expected to run in acceptable time. For the same problem, they have proposed approximation algorithms one with ratio 3/2 and two with ratio 5/3.…”

Section: Introductionmentioning

confidence: 99%

Offline first fit scheduling in smart grids

Ranjan

Khargonekar

Sahni

2015

2015 IEEE Symposium on Computers and Communication (ISCC)

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In this paper we consider the problem of scheduling energy consumption loads in the setting of smart electric grids. Each load is characterized as a "job" by a start (arrival) time and a deadline by which a certain amount of electric energy must be delivered to the load. A job may be preemptable, i. e., it can be interrupted or non-preemptable. Specifically, we focus on scheduling a mixture of preemptable and non-preemptable jobs with the same arrival time and deadline with the goal of minimizing the peak power. We study and modify the first fit decreasing height algorithm of the strip packing problem for this purpose. We derive a performance bound for the algorithm and prove its tightness. We test the performance of the algorithm extensively on a variety of datasets including real life household data.

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Smart-Grid Electricity Allocation via Strip Packing with Slicing

Cited by 18 publications

References 19 publications

Tight Approximation Algorithms for Geometric Bin Packing with Skewed Items

Tight Approximation Algorithms for Geometric Bin Packing with Skewed Items

Non-preemptive Scheduling in a Smart Grid Model and its Implications on Machine Minimization

Offline first fit scheduling in smart grids

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