Searching Monotone Multi-dimensional Arrays

TL;DR

This paper extends the search algorithm for monotone multi-dimensional arrays from 3D to higher dimensions, providing an asymptotically optimal solution for 4D arrays, advancing the understanding of efficient search in high-dimensional data structures.

Contribution

It generalizes the existing 3D search algorithm to d-dimensions for d≥4 and establishes asymptotic optimality for 4D arrays.

Findings

Extended the search algorithm to d-dimensional arrays for d≥4

Proved asymptotic optimality of the new algorithm for 4D arrays

Enhanced understanding of high-dimensional monotone array search complexity

Abstract

In this paper we investigate the problem of searching monotone multi-dimensional arrays. We generalize Linial and Saks' search algorithm \cite{LS1} for monotone 3-dimensional arrays to $d$-dimensions with $d\geq 4$. Our new search algorithm is asymptotically optimal for $d=4$.