Dynamic Trees with Almost-Optimal Access Cost

06/27/2018
by   Mordecai Golin, et al.
0

An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost optimal search trees. There exists a long literature of constructing almost optimal search trees dynamically, i.e., when the access pattern is not known in advance. All of these trees, e.g., splay trees and treaps, provide a multiplicative approximation to the optimal search cost. In this paper we show how to maintain an almost optimal weighted binary search tree under access operations and insertions of new elements where the approximation is an additive constant. More technically, we maintain a tree in which the depth of the leaf holding an element e_i does not exceed ((W/w_i), n)+O(1) where w_i is the number of times e_i was accessed and W is the total length of the access sequence. Our techniques can also be used to encode a sequence of m symbols with a dynamic alphabetic code in O(m) time so that the encoding length is bounded by m(H+O(1)), where H is the entropy of the sequence. This is the first efficient algorithm for adaptive alphabetic coding that runs in constant time per symbol.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/16/2022

Fast approximation of search trees on trees with centroid trees

Search trees on trees (STTs) generalize the fundamental binary search tr...
research
10/03/2018

Weighted dynamic finger in binary search trees

It is shown that the online binary search tree data structure GreedyASS ...
research
03/01/2021

On the Cost of Unsuccessful Searches in Search Trees with Two-way Comparisons

Search trees are commonly used to implement access operations to a set o...
research
12/26/2020

Arithmetic Binary Search Trees: Static Optimality in the Matching Model

Motivated by recent developments in optical switching and reconfigurable...
research
09/28/2017

Energy Constrained Depth First Search

Depth first search is a natural algorithmic technique for constructing a...
research
07/12/2018

Push-Down Trees: Optimal Self-Adjusting Complete Trees

Since Sleator and Tarjan's seminal work on self-adjusting lists, heaps a...
research
08/01/2019

Dynamic Optimality Refuted -- For Tournament Heaps

We prove a separation between offline and online algorithms for finger-b...

Please sign up or login with your details

Forgot password? Click here to reset