Concept

Submodular set function

Related publications (24)

Approximation Algorithms for Allocation and Network Design

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

EPFL2023

Streaming and Matching Problems with Submodular Functions

Paritosh Garg

Submodular functions are a widely studied topic in theoretical computer science. They have found several applications both theoretical and practical in the fields of economics, combinatorial optimization and machine learning. More recently, there have also ...

EPFL2022

Online Contention Resolution Schemes With Applications To Bayesian Selection Problems

Ola Nils Anders Svensson, Moran Feldman, Rico Zenklusen

We introduce a new rounding technique designed for online optimization problems, which is related to contention resolution schemes, a technique initially introduced in the context of submodular function maximization. Our rounding technique, which we call o ...

2021

A comment on performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid

Maryam Kamgarpour, Baiwei Guo, Orcun Karaca

We provide a counterexample to the performance guarantee obtained in the paper "Il'ev, V., Linker, N., 2006. Performance guarantees of a greedy algorithm for minimizing a supermodular set function on comatroid", which was published in Volume 171 of the Eur ...

ELSEVIER2021

The One-Way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness

Ola Nils Anders Svensson, Moran Feldman, Rico Zenklusen, Ashkan Norouzi Fard

We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multi-player model t ...

ASSOC COMPUTING MACHINERY2020

Robust Adaptive Decision Making: Bayesian Optimization and Beyond

Ilija Bogunovic

The central task in many interactive machine learning systems can be formalized as the sequential optimization of a black-box function. Bayesian optimization (BO) is a powerful model-based framework for \emph{adaptive} experimentation, where the primary go ...

EPFL2019

An Improved Analysis of Local Search for Max-Sum Diversification

Friedrich Eisenbrand, Rico Zenklusen, Alfonso Bolívar Cevallos Manzano

We present new techniques to analyze natural local search algorithms for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given an n-point set X subset of R-d and an integer k, select k points in X so th ...

INFORMS2019

Entropic Matroids and Their Representation

Emmanuel Abbé

This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p. We draw ...

2019

Robust Maximization of Non-Submodular Objectives

Volkan Cevher, Ilija Bogunovic, Junyao Zhao

We study the problem of maximizing a monotone set function subject to a cardinality constraint k in the setting where some number of elements is deleted from the returned set. The focus of this work is on the worst-case adversarial setting. While there exi ...

2018

Deterministic Algorithms for Submodular Maximization Problems

Moran Feldman

Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area, most algorithms are randomized, and in almost all c ...

ASSOC COMPUTING MACHINERY2018

A Framework for the Secretary Problem on the Intersection of Matroids

Ola Nils Anders Svensson, Moran Feldman, Rico Zenklusen

The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where elements arrive one- ...

ASSOC COMPUTING MACHINERY2018

Information Gathering with Peers: Submodular Optimization with Peer-Prediction Constraints

Boi Faltings, Goran Radanovic, Andreas Krause

We study a problem of optimal information gathering from multiple data providers that need to be incentivized to provide accurate information. This problem arises in many real world applications that rely on crowdsourced data sets, but where the process of ...

ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE2018

Maximizing Symmetric Submodular Functions

Moran Feldman

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases, including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little attention by c ...

Association for Computing Machinery2017

Optimal Approximation for Submodular and Supermodular Optimization with Bounded Curvature

Justin Dean Ward

We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a monotone increasing submodular function or ...

INFORMS2017

Subdeterminant Maximization via Nonconvex Relaxations and Anti-Concentration

Nisheeth Vishnoi, Javad Ebrahimi Boroojeni, Damian Mateusz Straszak

Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors v(1), ..., v(m) is an element of R-d and a constraint family B subset of 2([m]), find a set S. B that maximizes the squared volume of the sim ...

Ieee2017

Maximizing k-Submodular Functions and Beyond

Justin Dean Ward

We consider the maximization problem in the value oracle model of functions defined on k-tuples of sets that are submodular in every orthant and r-wise monotone, where k >= 2 and 1

Assoc Computing Machinery2016

A New Framework for Distributed Submodular Maximization

Justin Dean Ward

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing distributed algo ...

Ieee2016

Approximation algorithms for geometric dispersion

Alfonso Bolívar Cevallos Manzano

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...

EPFL2016

On the Complexity of Scheduling in Half-Duplex Diamond Networks

Christina Fragouli, Ayfer Özgür Aydin, Siddhartha Brahma

We consider an n-relay Gaussian diamond network where a source communicates to a destination with the help of n half-duplex relays. Achieving rates close to the capacity of this network requires to employ all the n relays under an optimal transmit/receive ...

Ieee-Inst Electrical Electronics Engineers Inc2016

An Efficient Streaming Algorithm for the Submodular Cover Problem

Volkan Cevher, Ilija Bogunovic, Ya-Ping Hsieh, Ashkan Norouzi Fard, Abbas Bazzi, Marwa El Halabi

We initiate the study of the classical Submodular Cover (SC) problem in the data streaming model which we refer to as the Streaming Submodular Cover (SSC). We show that any single pass streaming algorithm using sublinear memory in the size of the stream wi ...

2016