A generalized Cheeger inequality

被引：1
|
作者：
Koutis, Ioannis [1 ]
Miller, Gary [2 ]
Peng, Richard [3 ]
机构：
[1] New Jersey Inst Technol, Dept Comp Sci, Newark, NJ 07102 USA
[2] Carnegie Mellon Univ, Comp Sci Dept, Pittsburgh, PA USA
[3] Univ Waterloo, Cheriton Sch Comp Sci, Waterloo, ON, Canada
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 665卷
基金：
美国国家科学基金会;
关键词：
Spectral graph theory; Generalized cuts; Cheeger inequality; ISOPERIMETRIC-INEQUALITIES;
D O I：
10.1016/j.laa.2023.01.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The generalized conductance phi(G, H) between two weighted graphs G and H on the same vertex set V is defined as the ratio phi(G, H) = min S subset of V capG(S, S) capH(S, S over line ), where capG(S, S) is the total weight of the edges crossing from vertex set S subset of V to S over line = V - S. We show that the minimum generalized eigenvalue lambda(LG, LH) of the pair of Laplacians LG and LH satisfies phi(G, H) > lambda(LG, LH) > phi(G, H)phi(G)/16, where phi(G) is the standard conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to lambda(LG, LH).(c) 2023 Elsevier Inc. All rights reserved.
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页码：139 / 152
页数：14
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