Timezone: »
Choosing a diverse subset of a large collection of points in a metric space is a fundamental problem, with applications in feature selection, recommender systems, web search, data summarization, etc. Various notions of diversity have been proposed, tailored to different applications. The general algorithmic goal is to find a subset of points that maximize diversity, while obeying a cardinality (or more generally, matroid) constraint. The goal of this paper is to develop a novel linear programming (LP) framework that allows us to design approximation algorithms for such problems. We study an objective known as {\em sum-min} diversity, which is known to be effective in many applications, and give the first constant factor approximation algorithm. Our LP framework allows us to easily incorporate additional constraints, as well as secondary objectives. We also prove a hardness result for two natural diversity objectives, under the so-called {\em planted clique} assumption. Finally, we study the empirical performance of our algorithm on several standard datasets. We first study the approximation quality of the algorithm by comparing with the LP objective. Then, we compare the quality of the solutions produced by our method with other popular diversity maximization algorithms.
Author Information
Aditya Bhaskara (University of Utah)
Mehrdad Ghadiri (Sharif University of Technolog)
Vahab Mirrokni (Google)
Ola Svensson (EPFL)
More from the Same Authors
-
2023 Poster: Tight Bounds for Volumetric Spanners and Applications »
Aditya Bhaskara · Sepideh Mahabadi · Ali Vakilian -
2021 Poster: Nearly-Tight and Oblivious Algorithms for Explainable Clustering »
Buddhima Gamlath · Xinrui Jia · Adam Polak · Ola Svensson -
2021 Poster: Parallel and Efficient Hierarchical k-Median Clustering »
Vincent Cohen-Addad · Silvio Lattanzi · Ashkan Norouzi-Fard · Christian Sohler · Ola Svensson -
2021 Poster: Logarithmic Regret from Sublinear Hints »
Aditya Bhaskara · Ashok Cutkosky · Ravi Kumar · Manish Purohit -
2020 Poster: The Primal-Dual method for Learning Augmented Algorithms »
Etienne Bamas · Andreas Maggiori · Ola Svensson -
2020 Oral: The Primal-Dual method for Learning Augmented Algorithms »
Etienne Bamas · Andreas Maggiori · Ola Svensson -
2020 Poster: Adaptive Probing Policies for Shortest Path Routing »
Aditya Bhaskara · Sreenivas Gollapudi · Kostas Kollias · Kamesh Munagala -
2020 Poster: Optimal Approximation - Smoothness Tradeoffs for Soft-Max Functions »
Alessandro Epasto · Mohammad Mahdian · Vahab Mirrokni · Emmanouil Zampetakis -
2020 Spotlight: Optimal Approximation - Smoothness Tradeoffs for Soft-Max Functions »
Alessandro Epasto · Mohammad Mahdian · Vahab Mirrokni · Emmanouil Zampetakis -
2020 Poster: Online Linear Optimization with Many Hints »
Aditya Bhaskara · Ashok Cutkosky · Ravi Kumar · Manish Purohit -
2020 Poster: Learning Augmented Energy Minimization via Speed Scaling »
Etienne Bamas · Andreas Maggiori · Lars Rohwedder · Ola Svensson -
2020 Poster: Fast and Accurate $k$-means++ via Rejection Sampling »
Vincent Cohen-Addad · Silvio Lattanzi · Ashkan Norouzi-Fard · Christian Sohler · Ola Svensson -
2020 Poster: Online MAP Inference of Determinantal Point Processes »
Aditya Bhaskara · Amin Karbasi · Silvio Lattanzi · Morteza Zadimoghaddam -
2020 Spotlight: Learning Augmented Energy Minimization via Speed Scaling »
Etienne Bamas · Andreas Maggiori · Lars Rohwedder · Ola Svensson -
2020 Poster: Smoothly Bounding User Contributions in Differential Privacy »
Alessandro Epasto · Mohammad Mahdian · Jieming Mao · Vahab Mirrokni · Lijie Ren -
2020 Poster: Contextual Reserve Price Optimization in Auctions via Mixed Integer Programming »
Joey Huchette · Haihao Lu · Hossein Esfandiari · Vahab Mirrokni -
2020 : Clustering At Scale »
Vahab Mirrokni -
2020 Expo Workshop: Mining and Learning with Graphs at Scale »
Vahab Mirrokni · Bryan Perozzi · Jakub Lacki · Jonathan Halcrow · Jaqui C Herman -
2020 : Introduction »
Vahab Mirrokni -
2019 Poster: On Distributed Averaging for Stochastic k-PCA »
Aditya Bhaskara · Pruthuvi Maheshakya Wijewardena -
2019 Poster: Contextual Bandits with Cross-Learning »
Santiago Balseiro · Negin Golrezaei · Mohammad Mahdian · Vahab Mirrokni · Jon Schneider -
2019 Poster: Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions »
Negin Golrezaei · Adel Javanmard · Vahab Mirrokni -
2019 Poster: A Robust Non-Clairvoyant Dynamic Mechanism for Contextual Auctions »
Yuan Deng · Sébastien Lahaie · Vahab Mirrokni -
2019 Poster: Locality-Sensitive Hashing for f-Divergences: Mutual Information Loss and Beyond »
Lin Chen · Hossein Esfandiari · Gang Fu · Vahab Mirrokni -
2019 Poster: Greedy Sampling for Approximate Clustering in the Presence of Outliers »
Aditya Bhaskara · Sharvaree Vadgama · Hong Xu -
2019 Poster: Variance Reduction in Bipartite Experiments through Correlation Clustering »
Jean Pouget-Abadie · Kevin Aydin · Warren Schudy · Kay Brodersen · Vahab Mirrokni -
2017 Poster: Dynamic Revenue Sharing »
Santiago Balseiro · Max Lin · Vahab Mirrokni · Renato Leme · IIIS Song Zuo -
2017 Poster: Affinity Clustering: Hierarchical Clustering at Scale »
Mohammadhossein Bateni · Soheil Behnezhad · Mahsa Derakhshan · MohammadTaghi Hajiaghayi · Raimondas Kiveris · Silvio Lattanzi · Vahab Mirrokni -
2016 Poster: Bi-Objective Online Matching and Submodular Allocations »
Hossein Esfandiari · Nitish Korula · Vahab Mirrokni -
2014 Poster: Distributed Balanced Clustering via Mapping Coresets »
Mohammadhossein Bateni · Aditya Bhaskara · Silvio Lattanzi · Vahab Mirrokni