An Algorithm to Recover Shredded Random Matrices

IF 0.9 3区数学 Q2 MATHEMATICS SIAM Journal on Discrete Mathematics Pub Date : 2024-09-18 DOI:10.1137/23m1615784

Caelan Atamanchuk, Luc Devroye, Massimo Vicenzo

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2509-2529, September 2024.
Abstract. Given some binary matrix [math], suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, can we recover the unique original orderings and matrix? We present an algorithm that identifies whether there is a unique ordering associated with a set of rows and columns, and outputs either the unique correct orderings for the rows and columns or the full collection of all valid orderings and valid matrices. We show that there is a constant [math] such that the algorithm terminates in [math] time with high probability and in expectation for random [math] binary matrices with i.i.d. entries [math] such that [math] and [math].

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恢复破碎随机矩阵的算法

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2509-2529 页，2024 年 9 月。摘要。给定一个二元矩阵[math]，假设我们得到了它的行和列的独立任意排序集合。从这些信息中，我们能否恢复唯一的原始排序和矩阵？我们提出了一种算法，它能识别是否存在与一组行列相关的唯一排序，并输出行列的唯一正确排序或所有有效排序和有效矩阵的完整集合。我们证明，存在一个常数[math]，对于具有 i.i.d. 项[math]的随机[math]二进制矩阵[math]，即[math]和[math]，该算法可以在[math]时间内以高概率和期望值终止。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.

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