
A Matrix TrickleDown Theorem on Simplicial Complexes and Applications to Sampling Colorings
We show that the natural Glauber dynamics mixes rapidly and generates a ...
read it

A (Slightly) Improved Bound on the Integrality Gap of the Subtour LP for TSP
We show that for some ϵ > 10^36 and any metric TSP instance, the max en...
read it

Counting and Sampling Perfect Matchings in Regular Expanding NonBipartite Graphs
We show that the ratio of the number of near perfect matchings to the nu...
read it

An Improved Approximation Algorithm for the Minimum kEdge Connected MultiSubgraph Problem
We give a randomized 1+√(8ln k/k)approximation algorithm for the minimu...
read it

A (Slightly) Improved Approximation Algorithm for Metric TSP
For some ϵ > 10^36 we give a 3/2ϵ approximation algorithm for metric T...
read it

LogConcave Polynomials IV: Exchange Properties, Tight Mixing Times, and Faster Sampling of Spanning Trees
We prove tight mixing time bounds for natural random walks on bases of m...
read it

Spectral Independence in HighDimensional Expanders and Applications to the Hardcore Model
We say a probability distribution μ is spectrally independent if an asso...
read it

An Improved Approximation Algorithm for TSP in the Half Integral Case
We design a 1.49993approximation algorithm for the metric traveling sal...
read it

Composable Coresets for Determinant Maximization: A Simple NearOptimal Algorithm
"Composable coresets" are an efficient framework for solving optimizati...
read it

LogConcave Polynomials II: HighDimensional Walks and an FPRAS for Counting Bases of a Matroid
We use recent developments in the area of high dimensional expanders and...
read it

LogConcave Polynomials III: Mason's UltraLogConcavity Conjecture for Independent Sets of Matroids
We give a selfcontained proof of the strongest version of Mason's conje...
read it

A Polynomial Time MCMC Method for Sampling from Continuous DPPs
We study the Gibbs sampling algorithm for continuous determinantal point...
read it

Composable Coresets for Determinant Maximization Problems via Spectral Spanners
We study a spectral generalization of classical combinatorial graph span...
read it

Logconcave polynomials, entropy, and a deterministic approximation algorithm for counting bases of matroids
We give a deterministic polynomial time 2^O(r)approximation algorithm f...
read it

On the Bias of ReedMuller Codes over Odd Prime Fields
We study the bias of random boundeddegree polynomials over odd prime fi...
read it

Graph Clustering using Effective Resistance
#1#1 We design a polynomial time algorithm that for any weighted undire...
read it

A Simply Exponential Upper Bound on the Maximum Number of Stable Matchings
Stable matching is a classical combinatorial problem that has been the s...
read it

TimeSpace Tradeoffs for Learning from Small Test Spaces: Learning Low Degree Polynomial Functions
We develop an extension of recently developed methods for obtaining time...
read it

Partitioning into Expanders
Let G=(V,E) be an undirected graph, lambda_k be the kth smallest eigenv...
read it

Improved Cheeger's Inequality: Analysis of Spectral Partitioning Algorithms through Higher Order Spectral Gap
Let ϕ(G) be the minimum conductance of an undirected graph G, and let 0=...
read it
Shayan Oveis Gharan
is this you? claim profile