Smart-Grid Electricity Allocation via Strip Packing with Slicing

  • Soroush Alamdari
  • Therese Biedl
  • Timothy M. Chan
  • Elyot Grant
  • Krishnam Raju Jampani
  • Srinivasan Keshav
  • Anna Lubiw
  • Vinayak Pathak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)


One advantage of smart grids is that they can reduce the peak load by distributing electricity-demands over multiple short intervals. Finding a schedule that minimizes the peak load corresponds to a variant of a strip packing problem. Normally, for strip packing problems, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of the strip. The electricity-allocation application can be modelled as strip packing with slicing: each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. The stacking constraint forbids solutions in which a vertical line intersects two slices of the same rectangle.

We give a fully polynomial time approximation scheme for this problem, as well as a practical polynomial time algorithm that slices each rectangle at most once and yields a solution of height at most 5/3 times the optimal height.


Peak Load Smart Grid Packing Problem Optimal Height Strip Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Baker, B.S., Coffman, E.G., Rivest, R.L.: Orthogonal packings in two dimensions. SIAM Journal on Computing 9(4), 846–855 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bougeret, M., Dutot, P.F., Jansen, K., Otte, C., Trystram, D.: Approximating the non-contiguous multiple organization packing problem. In: Calude, C.S., Sassone, V. (eds.) TCS 2010. IFIP AICT, vol. 323, pp. 316–327. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Chen, B., Potts, C.N., Woeginger, G.J.: A review of machine scheduling: complexity, algorithms and approximability. In: Handbook of Combinatorial Optimization, vol. 3, pp. 21–169. Kluwer Acad. Publ., Boston (1998)Google Scholar
  4. 4.
    Coffman Jr., E.G., Garey, M.R., Johnson, D.S., Tarjan, R.E.: Performance bounds for level-oriented two-dimensional packing algorithms. SIAM J. Comput. 9(4), 808–826 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman & Co. Ltd. (1979)Google Scholar
  6. 6.
    Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting-stock problem. Operations Res. 9, 849–859 (1961)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Giudice, P.: Our energy future and smart grid communications. Testimony before the FCC Field Hearing on Energy and Environment (2009),
  8. 8.
    Graham, R.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Harren, R., Jansen, K., Prädel, L., van Stee, R.: A (5/3 + ε)-approximation for strip packing. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 475–487. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems: theoretical and practical results. J. Assoc. Comput. Mach. 34(1), 144–162 (1987)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jansen, K., Solis-Oba, R.: New approximability results for 2-dimensional packing problems. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 103–114. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Karmarkar, N., Karp, R.M.: An efficient approximation scheme for the one-dimensional bin-packing problem. In: Symposium on Foundations of Computer Science, pp. 312–320. IEEE (1982)Google Scholar
  13. 13.
    Kenyon, C., Rémila, E.: A near-optimal solution to a two-dimensional cutting stock problem. Math. Oper. Res. 25(4), 645–656 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems: A survey. European Journal of Operational Research 141(2), 241–252 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Sahni, S.K.: Algorithms for scheduling independent tasks. J. Assoc. Comput. Mach. 23(1), 116–127 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Schiermeyer, I.: Reverse-Fit: A 2-optimal algorithm for packing rectangles. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 290–299. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  17. 17.
    Sleator, D.D.: A 2.5 times optimal algorithm for packing in two dimensions. Information Processing Letters 10(1), 37–40 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Srikantha, P., Rosenberg, C., Keshav, S.: An analysis of peak demand reductions due to elasticity of omestic appliances. In: Proc. Energy-Efficient Computing and Networking (e-Energy 2012), p. 28. ACM (2012)Google Scholar
  19. 19.
    Steinberg, A.: A strip-packing algorithm with absolute performance bound 2. SIAM Journal on Computing 26(2), 401–409 (1997)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Soroush Alamdari
    • 1
  • Therese Biedl
    • 1
  • Timothy M. Chan
    • 1
  • Elyot Grant
    • 2
  • Krishnam Raju Jampani
    • 3
  • Srinivasan Keshav
    • 1
  • Anna Lubiw
    • 1
  • Vinayak Pathak
    • 1
  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.University of GuelphGuelphCanada

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