发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; University of Chinese Academy of Sciences（中国科学院数学与系统科学研究院; 中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出确定性多项式时间算法，为最大度Δ≥3的二分图赋符号，使符号邻接矩阵算子范数严格小于2√(Δ-1)，基于递归修复框架并采用确定性规则。
AI 中文摘要
我们针对二分图上的Bilu--Linial符号赋值问题给出一个确定性多项式时间算法。对于每个最大度数至多为整数Δ≥3的有限简单二分图，该算法为其边赋符号，使得符号邻接矩阵的算子范数严格小于2√(Δ-1)。我们的算法基于Jadbabaie、Saberi和Sra~\ncite{JSS26}的随机递归修复框架，并采用确定性的符号选择与顶点删除规则。
英文摘要
We give a deterministic polynomial-time algorithm for the Bilu--Linial signing problem on bipartite graphs. For every finite simple bipartite graph of maximum degree at most an integer $Δ\ge3$, the algorithm assigns signs to its edges so that the signed adjacency matrix has operator norm strictly less than $2\sqrt{Δ-1}$. Our algorithm builds on the randomized recursive repair framework of Jadbabaie, Saberi, and Sra~\cite{JSS26}, with deterministic rules for sign selection and vertex deletion.
Comments18 pages
