Approximation Algorithms for Demand Strip Packing

In the Demand Strip Packing problem (DSP), we are given a time interval and a collection of tasks, each characterized by a processing time and a demand for a given resource (such as electricity, computational power, etc.). A feasible solution consists of a schedule of the tasks within the mentioned time interval. Our goal is to minimize the peak resource consumption, i.e. the maximum total demand of tasks executed at any point in time. It is known that DSP is NP-hard to approximate below a factor 3/2, and standard techniques for related problems imply a (polynomial-time) 2-approximation. Our main result is a (5/3 + ε)approximation algorithm for any constant ε > 0. We also achieve best-possible approximation factors for some relevant special cases. Email: galvez@in.tum.de Supported by the European Research Council, Grant Agreement No. 691672, project APEG. Email: fabrizio@idsia.ch. Partially supported by the SNF Excellence Grant 200020B_182865. Email: afrouz@idsia.ch Email: kamyar.khodamoradi@uni-wuerzburg.de Partially supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Project number 399223600. This project was carried out in part when the author was a postdoctoral researcher at IDSIA, USI-SUPSI, Switzerland.

[1]  Brendan Mumey,et al.  Scheduling Non-Preemptible Jobs to Minimize Peak Demand , 2017, Algorithms.

[2]  Prudence W. H. Wong,et al.  Non-preemptive Scheduling in a Smart Grid Model and Its Implications on Machine Minimization , 2016, Algorithmica.

[3]  Ingo Schiermeyer,et al.  Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles , 1994, ESA.

[4]  Klaus Jansen,et al.  Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing , 2019, Theory of Computing Systems.

[5]  Rob van Stee,et al.  Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems , 2009, APPROX-RANDOM.

[6]  Amit Kumar,et al.  New Approximation Schemes for Unsplittable Flow on a Path , 2015, SODA.

[7]  Fabrizio Grandoni,et al.  Improved Approximation Algorithms for Unsplittable Flow on a Path with Time Windows , 2015, WAOA.

[8]  Timothy M. Chan,et al.  Smart-Grid Electricity Allocation via Strip Packing with Slicing , 2013, WADS.

[9]  Edward G. Coffman,et al.  Computer and job-shop scheduling theory , 1976 .

[10]  Mikkel Thorup,et al.  OPT versus LOAD in dynamic storage allocation , 2003, STOC '03.

[11]  Brendan Mumey,et al.  Peak demand scheduling in the Smart Grid , 2014, 2014 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[12]  Daniele Vigo,et al.  Bin packing approximation algorithms: Survey and classification , 2013 .

[13]  Klaus Jansen,et al.  A (5/3 + ε)-approximation for strip packing , 2014, Comput. Geom..

[14]  A. Steinberg,et al.  A Strip-Packing Algorithm with Absolute Performance Bound 2 , 1997, SIAM J. Comput..

[15]  Klaus Jansen,et al.  Closing the gap for pseudo-polynomial strip packing , 2017, ESA.

[16]  Klaus Jansen,et al.  Improved Approximation for Two Dimensional Strip Packing with Polynomial Bounded Width , 2017, WALCOM.

[17]  Klaus Jansen,et al.  Approximation Algorithms for Scheduling Parallel Jobs , 2010, SIAM J. Comput..

[18]  Robert E. Tarjan,et al.  Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms , 1980, SIAM J. Comput..

[19]  Ronald L. Rivest,et al.  Orthogonal Packings in Two Dimensions , 1980, SIAM J. Comput..

[20]  Maciej Drozdowski,et al.  On contiguous and non-contiguous parallel task scheduling , 2015, J. Sched..

[21]  Michal Pilipczuk,et al.  Hardness of Approximation for Strip Packing , 2017, TOCT.

[22]  Andreas Wiese,et al.  A quasi-PTAS for the Two-Dimensional Geometric Knapsack Problem , 2015, SODA.

[23]  Klaus Jansen,et al.  Rectangle packing with one-dimensional resource augmentation , 2009, Discret. Optim..

[24]  Pierre-François Dutot,et al.  Scheduling Parallel Tasks Approximation Algorithms , 2004, Handbook of Scheduling.

[25]  Claire Mathieu,et al.  A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem , 2000, Math. Oper. Res..

[26]  Hsiang-Hsuan Liu,et al.  Greedy is Optimal for Online Restricted Assignment and Smart Grid Scheduling for Unit Size Jobs , 2019, Theory of Computing Systems.

[27]  Klaus Jansen,et al.  A(3/2+ε) approximation algorithm for scheduling moldable and non-moldable parallel tasks , 2012, SPAA '12.

[28]  Andreas Wiese,et al.  Breaking the Barrier of 2 for the Storage Allocation Problem , 2019, ICALP.

[29]  Klaus Jansen,et al.  A Tight $$(3/2+\varepsilon )$$ ( 3 / 2 + ε ) , 2023, Algorithmica.

[30]  Daniel Dominic Sleator,et al.  A 2.5 Times Optimal Algorithm for Packing in Two Dimensions , 1980, Inf. Process. Lett..

[31]  Fabrizio Grandoni,et al.  Improved Pseudo-Polynomial-Time Approximation for Strip Packing , 2018, FSTTCS.

[32]  Fabrizio Grandoni,et al.  A (5/3 + ε)-approximation for unsplittable flow on a path: placing small tasks into boxes , 2018, STOC.

[33]  Mihai Burcea,et al.  Scheduling for Electricity Cost in Smart Grid , 2013, COCOA.

[34]  Klaus Jansen,et al.  Peak Demand Minimization via Sliced Strip Packing , 2021, APPROX-RANDOM.

[35]  Joseph Y.-T. Leung,et al.  Packing Squares into a Square , 1990, J. Parallel Distributed Comput..

[36]  Giorgi Nadiradze,et al.  On approximating strip packing with a better ratio than 3/2 , 2016, SODA.

[37]  Fabrizio Grandoni,et al.  Approximating Geometric Knapsack via L-Packings , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).

[38]  Sartaj Sahni,et al.  Offline first fit scheduling in smart grids , 2015, 2015 IEEE Symposium on Computers and Communication (ISCC).

[39]  Shaojie Tang,et al.  Smoothing the energy consumption: Peak demand reduction in smart grid , 2013, 2013 Proceedings IEEE INFOCOM.

[40]  Yuval Rabani,et al.  An improved approximation algorithm for resource allocation , 2011, TALG.

[41]  Klaus Jansen,et al.  A Structural Lemma in 2-Dimensional Packing, and Its Implications on Approximability , 2009, ISAAC.

[42]  Ioannis Lambadaris,et al.  Power strip packing of malleable demands in smart grid , 2013, 2013 IEEE International Conference on Communications (ICC).

[43]  Fabrizio Grandoni,et al.  A Mazing 2+∊ Approximation for Unsplittable Flow on a Path , 2014, SODA.