Online Square Packing

Authors:
Sándor P. Fekete;Tom Kamphans;Nils Schweer
Affiliations:
Department of Computer Science, Algorithms Group, Braunschweig University of Technology, Braunschweig, Germany 38106;Department of Computer Science, Algorithms Group, Braunschweig University of Technology, Braunschweig, Germany 38106;Department of Computer Science, Algorithms Group, Braunschweig University of Technology, Braunschweig, Germany 38106
Venue:
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Year:
2009

Citing 6
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Abstract

We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time. The objective is to pack these items as they arrive, minimizing the resulting height. Just like in the classical game of Tetris, each square must be moved along a collision-free path to its final destination. In addition, we account for gravity in both motion and position. We apply a geometric analysis to establish a competitive factor of 3.5 for the bottom-left heuristic and present a $\frac{34}{13} \approx 2.6154$-competitive algorithm.