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We study the problem of maximizing a non-negative monotone submodular objective $f$ subject to the intersection of $k$ arbitrary matroid constraints. The natural greedy algorithm guarantees $(k+1)$-approximation for this problem, and the…

Data Structures and Algorithms · Computer Science 2026-05-11 Moran Feldman , Justin Ward

Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…

Machine Learning · Computer Science 2021-03-22 Rishabh Iyer

We improve the efficiency of algorithms for stochastic \emph{combinatorial semi-bandits}. In most interesting problems, state-of-the-art algorithms take advantage of structural properties of rewards, such as \emph{independence}. However,…

Machine Learning · Statistics 2019-06-24 Pierre Perrault , Vianney Perchet , Michal Valko

We initiate the study of matroid problems in a new oracle model called dynamic oracle. Our algorithms in this model lead to new bounds for some classic problems, and a "unified" algorithm whose performance matches previous results developed…

Data Structures and Algorithms · Computer Science 2023-04-28 Joakim Blikstad , Sagnik Mukhopadhyay , Danupon Nanongkai , Ta-Wei Tu

Maximizing a submodular function is a fundamental task in machine learning and in this paper we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the…

Data Structures and Algorithms · Computer Science 2025-05-26 Paul Dütting , Federico Fusco , Silvio Lattanzi , Ashkan Norouzi-Fard , Morteza Zadimoghaddam

Fast algorithms for submodular maximization problems have a vast potential use in applicative settings, such as machine learning, social networks, and economics. Though fast algorithms were known for some special cases, only recently…

Data Structures and Algorithms · Computer Science 2014-10-06 Niv Buchbinder , Moran Feldman , Roy Schwartz

Querying complex models for precise information (e.g. traffic models, database systems, large ML models) often entails intense computations and results in long response times. Thus, weaker models which give imprecise results quickly can be…

Data Structures and Algorithms · Computer Science 2024-11-06 Franziska Eberle , Felix Hommelsheim , Alexander Lindermayr , Zhenwei Liu , Nicole Megow , Jens Schlöter

This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems…

Data Structures and Algorithms · Computer Science 2025-01-03 Solmaz S. Kia

We study a submodular maximization problem motivated by applications in online retail. A platform displays a list of products to a user in response to a search query. The user inspects the first $k$ items in the list for a $k$ chosen at…

Computer Science and Game Theory · Computer Science 2022-10-24 Arash Asadpour , Rad Niazadeh , Amin Saberi , Ali Shameli

In this paper, we consider dynamic matroids, where elements can be inserted to or deleted from the ground set over time. The independent sets change to reflect the current ground set. As matroids are central to the study of many…

Data Structures and Algorithms · Computer Science 2026-02-10 Tijn de Vos , Mara Grilnberger

Estimating the linear dimensionality of a data set in the presence of noise is a common problem. However, data may also be corrupted by monotone nonlinear distortion that preserves the ordering of matrix entries but causes linear methods…

Combinatorics · Mathematics 2024-01-01 Caitlin Lienkaemper

We provide simple and fast polynomial time approximation schemes (PTASs) for several variants of the max-sum diversification problem which, in its most basic form, is as follows: Given n points p_1,...,p_n in R^d and an integer k, select k…

Data Structures and Algorithms · Computer Science 2016-07-18 Alfonso Cevallos , Friedrich Eisenbrand , Rico Zenklusen

We study budgeted variants of well known maximization problems with multiple matroid constraints. Given an $\ell$-matchoid $\cm$ on a ground set $E$, a profit function $p:E \rightarrow \mathbb{R}_{\geq 0}$, a cost function $c:E \rightarrow…

Data Structures and Algorithms · Computer Science 2023-07-11 Ilan Doron-Arad , Ariel Kulik , Hadas Shachnai

We introduce the parametric matroid one-interdiction problem. Given a matroid, each element of its ground set is associated with a weight that depends linearly on a real parameter from a given parameter interval. The goal is to find, for…

Combinatorics · Mathematics 2024-08-15 Nils Hausbrandt , Oliver Bachtler , Stefan Ruzika , Luca E. Schäfer

This paper provides a zeroth-order optimisation framework for non-smooth and possibly non-convex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of iterations required to ensure…

Optimization and Control · Mathematics 2021-06-29 Alejandro I. Maass , Chris Manzie , Iman Shames , Hayato Nakada

Combinatorial multi-armed bandits provide a fundamental online decision-making environment where a decision-maker interacts with an environment across $T$ time steps, each time selecting an action and learning the cost of that action. The…

Machine Learning · Computer Science 2026-04-13 Gerdus Benadè , Rathish Das , Thomas Lavastida

We present a formal analysis, in Isabelle/HOL, of optimisation algorithms for matroids, which are useful generalisations of combinatorial structures that occur in optimisation, and greedoids, which are a generalisation of matroids. Although…

Logic in Computer Science · Computer Science 2025-07-01 Mohammad Abdulaziz , Thomas Ammer , Shriya Meenakshisundaram , Adem Rimpapa

Submodular maximization constitutes a prominent research topic in combinatorial optimization and theoretical computer science, with extensive applications across diverse domains. While substantial advancements have been achieved in…

Data Structures and Algorithms · Computer Science 2026-03-17 Shengminjie Chen , Yiwei Gao , Kaifeng Lin , Xiaoming Sun , Jialin Zhang

Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary…

Data Structures and Algorithms · Computer Science 2024-02-20 Paul Dütting , Federico Fusco , Silvio Lattanzi , Ashkan Norouzi-Fard , Morteza Zadimoghaddam

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…

Artificial Intelligence · Computer Science 2012-09-26 Lirun Su , William Zhu