Our new paper has been published by Discrete Applied Mathematics Journal

Our new paper has been published by Discrete Applied Mathematics Journal

5/11/2016

Decision trees with minimum average depth for sorting eight elements

authors: Hassam AbouEisha, Igor Chikalov, Mikhail Moshkov

We prove that the minimum average depth of a decision tree for sorting 8 pairwise different elements is equal to 620160/8!. We show also that each decision tree for sorting 8 elements, which has minimum average depth (the number of such trees is approximately equal to 8.548 × 10^326365), has also minimum depth. Both problems were considered by Knuth (1998). To obtain these results, we use tools based on extensions of dynamic programming which allow us to make sequential optimization of decision trees relative to depth and average depth, and to count the number of decision trees with minimum average depth.