Dynamic data structures for twin-ordered matrices

TL;DR

This paper introduces a dynamic data structure for binary matrices that are twin-ordered, enabling efficient cell queries and updates with logarithmic double-logarithmic time complexity, optimized for fixed parameter d.

Contribution

The paper presents the first dynamic data structure for d-twin-ordered matrices supporting fast queries and updates with logarithmic double-logarithmic time complexity.

Findings

Supports cell queries and updates in O(log log n) expected time

Uses O_d(n) memory for representing matrices

Applicable to binary d-twin-ordered matrices

Abstract

We present a dynamic data structure for representing binary $n\times n$ matrices that are $d$-twin-ordered, for a~fixed parameter $d$. Our structure supports cell queries and single-cell updates both in $\Oh(\log \log n)$ expected worst case time, while using $\Oh_d(n)$ memory; here, the $\Oh_d(\cdot)$ notation