no code implementations • 2 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
no code implementations • 15 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
no code implementations • 6 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.
no code implementations • 20 Oct 2018 • Shayan Oveis Gharan, Alireza Rezaei
We study the Gibbs sampling algorithm for continuous determinantal point processes.
no code implementations • 31 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.
no code implementations • 2 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
no code implementations • 8 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.
no code implementations • 16 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.
no code implementations • 12 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.