A deterministic polynomial-time algorithm for the Bilu--Linial signing problem on bipartite graphs
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Xu, Zhiqiang
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220978589