Optimal Sublinear Sampling of Spanning Trees and Determinantal Point Processes via Average-Case Entropic Independence

no code implementations • 6 Apr 2022 • Nima Anari, Yang P. Liu, Thuy-Duong Vuong

We even improve the state of the art for obtaining a single sample from determinantal point processes, from the prior runtime of $\widetilde{O}(\min\{nk^2, n^\omega\})$ to $\widetilde{O}(nk^{\omega-1})$.

Point Processes

Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg-Rao

no code implementations • 18 Jan 2021 • Yu Gao, Yang P. Liu, Richard Peng

We give an algorithm for computing exact maximum flows on graphs with $m$ edges and integer capacities in the range $[1, U]$ in $\widetilde{O}(m^{\frac{3}{2} - \frac{1}{328}} \log U)$ time.

Data Structures and Algorithms

Minimum Cost Flows, MDPs, and $\ell_1$-Regression in Nearly Linear Time for Dense Instances

no code implementations • 14 Jan 2021 • Jan van den Brand, Yin Tat Lee, Yang P. Liu, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, Di Wang

In the special case of the minimum cost flow problem on $n$-vertex $m$-edge graphs with integer polynomially-bounded costs and capacities we obtain a randomized method which solves the problem in $\tilde{O}(m+n^{1. 5})$ time.

Data Structures and Algorithms Optimization and Control

Vertex Sparsification for Edge Connectivity in Polynomial Time

no code implementations • 30 Nov 2020 • Yang P. Liu

An important open question in the area of vertex sparsification is whether $(1+\epsilon)$-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist.

Data Structures and Algorithms