Online Weight Balancing on the Unit Circle

We consider a problem as follows: Given unit weights arriving in an online manner with the total cardinality unknown, upon each arrival we decide where to place it on the unit circle in $\mathbb{R}^{2}$. The objective is to set the center of mass of the placed weights as close to the origin as possi...

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Veröffentlicht in:IEICE Transactions on Information and Systems 2016/03/01, Vol.E99.D(3), pp.567-574
Hauptverfasser: FUJIWARA, Hiroshi, SEKI, Takahiro, FUJITO, Toshihiro
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Sprache:eng
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Zusammenfassung:We consider a problem as follows: Given unit weights arriving in an online manner with the total cardinality unknown, upon each arrival we decide where to place it on the unit circle in $\mathbb{R}^{2}$. The objective is to set the center of mass of the placed weights as close to the origin as possible. We apply competitive analysis defining the competitive difference as a performance measure. We first present an optimal strategy for placing unit weights which achieves a competitive difference of $\frac{1}{5}$. We next consider a variant in which the destination of each weight must be chosen from a set of positions that equally divide the unit circle. We give a simple strategy whose competitive difference is 0.35. Moreover, in the offline setting, several conditions for the center of mass to lie at the origin are derived.
ISSN:0916-8532
1745-1361
DOI:10.1587/transinf.2015FCP0006