Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decisionmaking and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning probability for a distinguished player, has received a lot of attention. Previous works consider the problem where the pairwise winning probabilities are known precisely, while we study how robust is the winning probability with respect to small errors in the pairwise winning probabilities. First, we present several illuminating examples to establish: (a) there exist deterministic tournaments (where the pairwise winning probabilities are 0 or 1) where one optimal draw is much more robust than the other; and (b) in general, there exist tournaments with slightly suboptimal draws that are more robust than all the optimal draws. The above examples motivate the study of the computational problem of robust draws that guarantee a specified winning probability. Second, we present a polynomial-time algorithm for approximating the robustness of a draw for sufficiently small errors in pairwise winning probabilities, and obtain that the stated computational problem is NP-complete. We also show that two natural cases of deterministic tournaments where the optimal draw could be computed in polynomial time also admit polynomial-time algorithms to compute robust optimal draws.
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IJCAI: International Joint Conference on Artificial Intelligence
New York, NY, USA
2016-07-09 – 2016-07-15
Chatterjee K, Ibsen-Jensen R, Tkadlec J. Robust draws in balanced knockout tournaments. In: Vol 2016-January. AAAI Press; 2016:172-179.
Chatterjee, K., Ibsen-Jensen, R., & Tkadlec, J. (2016). Robust draws in balanced knockout tournaments (Vol. 2016–January, pp. 172–179). Presented at the IJCAI: International Joint Conference on Artificial Intelligence, New York, NY, USA: AAAI Press.
Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Josef Tkadlec. “Robust Draws in Balanced Knockout Tournaments,” 2016–January:172–79. AAAI Press, 2016.
K. Chatterjee, R. Ibsen-Jensen, and J. Tkadlec, “Robust draws in balanced knockout tournaments,” presented at the IJCAI: International Joint Conference on Artificial Intelligence, New York, NY, USA, 2016, vol. 2016–January, pp. 172–179.
Chatterjee K, Ibsen-Jensen R, Tkadlec J. 2016. Robust draws in balanced knockout tournaments. IJCAI: International Joint Conference on Artificial Intelligence vol. 2016–January. 172–179.
Chatterjee, Krishnendu, et al. Robust Draws in Balanced Knockout Tournaments. Vol. 2016–January, AAAI Press, 2016, pp. 172–79.
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