A Generalized Cheeger Inequality

نویسندگان

Ioannis Koutis

Gary L. Miller

Richard Peng

چکیده

where capG(S, S̄) is the total weight of the edges crossing from S to S̄ = V − S. We show that the minimum generalized eigenvalue λ(LG, LH) of the pair of Laplacians LG and LH satisfies λ(LG, LH) ≥ φ(G,H)φ(G)/8, where φ(G) is the usual conductance of G. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to λ(LG, LH). The inequality complements a result of Trevisan [Tre13] which shows that φ(G) cannot be replaced by Θ(φ(G,H)) in the above inequality, unless the Unique Games Conjecture is false.

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