Optimal Leaf Ordering of Complete Binary Trees

Ordering a set of items so as to minimize the sum of distances between consecutive elements is a fundamental optimization problem occurring in many settings. While it is View the MathML source-hard in general, it becomes polynomially solvable if the set of feasible permutations is restricted to be compatible with a tree of bounded degree. We present a new algorithm for the elementary case of ordering the n leaves of a binary tree with height View the MathML source. Our algorithm requires View the MathML source time and View the MathML source space. While the running time is a log-factor away from being asymptotically optimal, the algorithm is conceptually simple, easy to implement, and highly practical. Its implementation requires little more than a few bit-manipulations