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Erschienen in:
01.01.2015
New bounds for the balloon popping problem
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 1/2015
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Abstract
We reconsider the balloon popping problem, an intriguing combinatorial problem introduced in order to bound the competitiveness of ascending auctions with anonymous bidders with respect to the best fixed-price scheme. Previous works show that the optimal solution for this problem is in the range (1.6595,2). We give a new lower bound of \(1.68\) and design an \(O(n^5)\) algorithm for computing upper bounds as a function of the number of bidders \(n\). Our algorithm provides an experimental evidence that the correct upper bound is a constant smaller than \(2\), thus disproving a currently believed conjecture, and can be used to test the validity of a new conjecture we propose, according to which the upper bound would decrease to \(\pi ^2/6+1/4\approx 1.8949\).