Abstract
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.
This work was done as part of an Algorithms Problem Session at the University of Waterloo. Research of TB, TC, SK and AL supported by NSERC.
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Alamdari, S. et al. (2013). Smart-Grid Electricity Allocation via Strip Packing with Slicing. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40104-6_3
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DOI: https://doi.org/10.1007/978-3-642-40104-6_3
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