Bounds and Algorithms for Alphabetic Codes and Binary Search Trees

TL;DR

This paper introduces new linear-time algorithms for alphabetic codes that are near-optimal and uses these results to derive improved bounds on the average cost of optimal binary search trees, advancing the understanding of these structures.

Contribution

It presents novel linear-time algorithms for alphabetic codes and leverages these to establish tighter bounds on binary search tree costs, a significant improvement over previous results.

Findings

New linear-time algorithms for alphabetic codes

Codes are close to optimal in cost

Improved bounds on binary search tree average cost

Abstract

Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes, and we show that the obtained codes are not too far from being optimal. Moreover, we exploit our results on alphabetic codes to provide new bounds on the average cost of optimal binary search trees. Our results improve on the best-known bounds on the average cost of optimal binary search trees present in the literature.