Dynamic data structures for twin-ordered matrices

2026-02-21

AI Summary

This work addresses the problem of efficiently supporting dynamic updates and queries on an $n \times n$ binary matrix that exhibits a twin-ordered structure under a fixed parameter $d$. The authors propose a dynamic indexing scheme based on compact data structures and hashing techniques, which exploits the structural properties inherent to twin-ordered matrices. The resulting data structure occupies only $O_d(n)$ space and achieves expected worst-case time complexity of $O(\log \log n)$ for both single-cell updates and queries. This approach significantly advances the state of the art in dynamic handling of twin-ordered matrices, delivering theoretical breakthroughs in both space efficiency and time performance.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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

Problem

• dynamic data structure
• twin-ordered matrix
• binary matrix
• cell query
• single-cell update

Innovation

• dynamic data structure
• twin-ordered matrix
• cell query
• single-cell update
• log log time