A note on searching sorted unbalanced three-dimensional arrays

TL;DR

This paper investigates optimal algorithms for searching a specific real value within a sorted, unbalanced three-dimensional array, focusing on minimizing the worst-case number of sequential queries needed.

Contribution

It introduces methods for constructing algorithms that efficiently determine the key with minimal queries in unbalanced 3D arrays.

Findings

Developed query-efficient search algorithms for unbalanced 3D arrays.

Provided bounds on the minimum number of queries needed in worst-case scenarios.

Addressed the challenge of variable array dimensions in search algorithms.

Abstract

We examine the problem of searching sequentially for a desired real value (a key) within a sorted unbalanced three-dimensional finite real array. This classic problem can be viewed as determining the correct dimensional threshold function from a finite class of such functions within the array, based on sequential queries that take the form of point samples. This note addresses the challenge of constructing algorithms that require the minimum number of queries necessary in the worst case, to search for a given key in arrays that have three dimensions with sizes that are not necessarily equal.