Spectral aspects of symmetric matrix signings

Charles Carlson, Karthekeyan Chandrasekaran, Hsien Chih Chang, Naonori Kakimura, Alexandra Kolla

研究成果: Conference contribution

抄録

The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of finding symmetric signings of matrices with natural spectral properties. Our results are the following: 1. We characterize matrices that have an invertible signing: a symmetric matrix has an invertible symmetric signing if and only if the support graph of the matrix contains a perfect 2-matching. Further, we present an efficient algorithm to search for an invertible symmetric signing. 2. We use the above-mentioned characterization to give an algorithm to find a minimum increase in the support of a given symmetric matrix so that it has an invertible symmetric signing. 3. We show NP-completeness of the following problems: verifying whether a given matrix has a symmetric signing that is singular or has bounded eigenvalues. However, we also illustrate that the complexity could differ substantially for input matrices that are adjacency matrices of graphs. We use combinatorial techniques in addition to classic results from matching theory.

本文言語English
ホスト出版物のタイトル44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
編集者Joost-Pieter Katoen, Pinar Heggernes, Peter Rossmanith
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(電子版)9783959771177
DOI
出版ステータスPublished - 2019 8
イベント44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019 - Aachen, Germany
継続期間: 2019 8 262019 8 30

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
138
ISSN(印刷版)1868-8969

Conference

Conference44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019
国/地域Germany
CityAachen
Period19/8/2619/8/30

ASJC Scopus subject areas

  • ソフトウェア

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