# A Quasipolynomial (2+epsilon)-Approximation for Planar Sparsest Cut

**Speaker**: Vincent Cohen-Addad (Google Zürich)

**Abstract:**
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total demand of the pairs separated by this deletion. Despite much effort, there are only a handful of nontrivial classes of supply graphs for which constant-factor approximations are known.
We consider the problem for planar graphs, and give a (2+epsilon)-approximation algorithm that runs in quasi-polynomial time. Our approach defines a new structural decomposition of an optimal solution using a "patching" primitive. We combine this decomposition with a Sherali-Adams-style linear programming relaxation of the problem, which we then round. This should be compared with the polynomial-time approximation algorithm of Rao (1999), which uses the metric linear programming relaxation and ell_1-embeddings, and achieves an O(sqrt(log n))-approximation in polynomial time.

Joint work with Anupam Gupta, Philip Klein, and Jason Li.

**Date and time:** 01/07/2021 at 14:30 (Paris time)

**Link to the talk:** https://bbb-temp.grenet.fr/b/lou-9x7-69p