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(n5) 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 π2/6+1/4≈1.8949.
New bounds for the balloon popping problem
Bilò Davide;
2015
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(n5) 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 π2/6+1/4≈1.8949.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
