Upper and Lower Bounds on Constructing Alphabetic Binary Trees

Abstract

This paper studies the long-standing open question of whether optimal alphabetic binary trees can be constructed in $o( n\lg n )$ time. We show that a class of techniques for finding optimal alphabetic trees which includes all current methods yielding $O( n\lg n )$-time algorithms are at least as hard as sorting in whatever model of computation is used. We also give $O( n )$-time algorithms for the case where all the input weights are within a constant factor of one another and when they are exponentially separated.