no code implementations • 15 Jun 2023 • Lap Chi Lau, Kam Chuen Tung, Robert Wang
We consider a new semidefinite programming relaxation for directed edge expansion, which is obtained by adding triangle inequalities to the reweighted eigenvalue formulation.
no code implementations • 3 May 2023 • Lap Chi Lau, Robert Wang, Hong Zhou
We prove that a randomized local search approach provides a unified algorithm to solve this problem for all $p$.
no code implementations • 17 Nov 2022 • Lap Chi Lau, Kam Chuen Tung, Robert Wang
The first main result is a Cheeger inequality relating the vertex expansion $\vec{\psi}(G)$ of a directed graph $G$ to the vertex-capacitated maximum reweighted second eigenvalue $\vec{\lambda}_2^{v*}$: \[ \vec{\lambda}_2^{v*} \lesssim \vec{\psi}(G) \lesssim \sqrt{\vec{\lambda}_2^{v*} \cdot \log (\Delta/\vec{\lambda}_2^{v*})}.
no code implementations • 29 Oct 2020 • Lap Chi Lau, Hong Zhou
We present a local search framework to design and analyze both combinatorial algorithms and rounding algorithms for experimental design problems.