A polynomial-time differentially private algorithm approximates every cut in a graph within (1+γ) multiplicative and n^{1.25+o(1)} additive error, breaking the previous n^{1.5} barrier.
Deterministic Weighted Expander Decomposition in Almost-linear Time
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abstract
In this note, we study the expander decomposition problem in a more general setting where the input graph has positively weighted edges and nonnegative demands on its vertices. We show how to extend the techniques of Chuzhoy et al. (FOCS 2020) to this wider setting, obtaining a deterministic algorithm for the problem in almost-linear time.
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Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition
A polynomial-time differentially private algorithm approximates every cut in a graph within (1+γ) multiplicative and n^{1.25+o(1)} additive error, breaking the previous n^{1.5} barrier.