Search Results for author: Shayan Oveis Gharan

Found 9 papers, 0 papers with code

A (Slightly) Improved Approximation Algorithm for Metric TSP

no code implementations2 Jul 2020 Anna R. Karlin, Nathan Klein, Shayan Oveis Gharan

For some $\epsilon > 10^{-36}$ we give a randomized $3/2-\epsilon$ approximation algorithm for metric TSP.

Data Structures and Algorithms Combinatorics Probability

Log-Concave Polynomials IV: Approximate Exchange, Tight Mixing Times, and Near-Optimal Sampling of Forests

no code implementations15 Apr 2020 Nima Anari, Kuikui Liu, Shayan Oveis Gharan, Cynthia Vinzant

For a matroid of rank $k$ on a ground set of $n$ elements, or more generally distributions associated with log-concave polynomials of homogeneous degree $k$ on $n$ variables, we show that the down-up random walk, started from an arbitrary point in the support, mixes in time $O(k\log k)$.

Data Structures and Algorithms Discrete Mathematics Probability

Composable Core-sets for Determinant Maximization: A Simple Near-Optimal Algorithm

no code implementations6 Jul 2019 Piotr Indyk, Sepideh Mahabadi, Shayan Oveis Gharan, Alireza Rezaei

In this work, first we provide a theoretical approximation guarantee of $O(C^{k^2})$ for the Greedy algorithm in the context of composable core-sets; Further, we propose to use a Local Search based algorithm that while being still practical, achieves a nearly optimal approximation bound of $O(k)^{2k}$; Finally, we implement all three algorithms and show the effectiveness of our proposed algorithm on standard data sets.

Fairness Point Processes

A Polynomial Time MCMC Method for Sampling from Continuous DPPs

no code implementations20 Oct 2018 Shayan Oveis Gharan, Alireza Rezaei

We study the Gibbs sampling algorithm for continuous determinantal point processes.

Point Processes

Composable Core-sets for Determinant Maximization Problems via Spectral Spanners

no code implementations31 Jul 2018 Piotr Indyk, Sepideh Mahabadi, Shayan Oveis Gharan, Alireza Rezaei

We show that for many objective functions one can use a spectral spanner, independent of the underlying functions, as a core-set and obtain almost optimal composable core-sets.

Log-Concave Polynomials I: Entropy and a Deterministic Approximation Algorithm for Counting Bases of Matroids

no code implementations2 Jul 2018 Nima Anari, Shayan Oveis Gharan, Cynthia Vinzant

We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$.

Data Structures and Algorithms Information Theory Combinatorics Information Theory Probability

Time-Space Tradeoffs for Learning from Small Test Spaces: Learning Low Degree Polynomial Functions

no code implementations8 Aug 2017 Paul Beame, Shayan Oveis Gharan, Xin Yang

We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space of inputs, a class of learning problems that is not handled by prior work.

Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes

no code implementations16 Feb 2016 Nima Anari, Shayan Oveis Gharan, Alireza Rezaei

Strongly Rayleigh distributions are natural generalizations of product and determinantal probability distributions and satisfy strongest form of negative dependence properties.

Open-Ended Question Answering Point Processes

Partitioning into Expanders

no code implementations12 Sep 2013 Shayan Oveis Gharan, Luca Trevisan

Unlike the recent results on higher order Cheeger's inequality [LOT12, LRTV12], our algorithmic results do not use higher order eigenfunctions of G. If there is a sufficiently large gap between lambda_k and lambda_{k+1}, more precisely, if \lambda_{k+1} >= \poly(k) lambda_{k}^{1/4} then our algorithm finds a k partitioning of V into sets P_1,..., P_k such that the induced subgraph G[P_i] has a significantly larger conductance than the conductance of P_i in G. Such a partitioning may represent the best k clustering of G. Our algorithm is a simple local search that only uses the Spectral Partitioning algorithm as a subroutine.

Clustering

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