# Seminars & Colloquia Calendar

## Set Cover in Sub-linear Time

#### Sepideh Mahabadi, Columbia University

Location: ** CoRE 301**

Date & time: Wednesday, 07 March 2018 at 11:00AM - 12:00PM

Abstract: Given access to a collection of \(m\) sets over a ground set of \(n\) elements, the classic set cover problem asks for the minimum number of sets in the collection that cover all the elements. We study this problem from the perspective of sub-linear algorithms, where the input can be accessed by querying either the ith element contained in a set, or the jth set containing an element. In this work, we present sub-linear algorithms for the set cover problem and show that they achieve almost tight query complexities.

More specifically, on the one hand, we show an algorithm that returns an \(alpha\)-approximate cover using \(tilde O(m(n/k)^{1/(alpha-1)} + nk)\) queries to the input, where \(k\) denotes the value of a minimum set cover. We then complement this upper bound by proving that for lower values of \(k\), the required number of queries is \(tilde Omega(m(n/k)^{1/(2alpha)})\). Moreover, we prove that even checking whether a given collection of sets covers all the elements would require \(Omega(nk)\) queries. These two lower bounds provide strong evidence that the upper bound is almost tight for certain values of the parameter \(k\). On the other hand, we show that this bound is not optimal for larger values of the parameter \(k\), as there exists a \((1+eps)\)-approximation algorithm with \(tilde O(mn/keps^2)\) queries. We show that this bound is also essentially tight by establishing a lower bound of \(tilde Omega(mn/k)\).

This is a joint work with Piotr Indyk, Ronitt Rubinfeld, Ali Vakilian, and Anak Yodpinyanee.

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Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

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