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We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

Data Structures and Algorithms · Computer Science 2022-11-16 Sungjin Im , Benjamin Moseley , Hung Q. Ngo , Kirk Pruhs , Alireza Samadian

Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…

Data Structures and Algorithms · Computer Science 2012-05-08 Niv Buchbinder , Joseph , Naor , R. Ravi , Mohit Singh

Matroid is a generalization of many fundamental objects in combinatorial mathematics , and matroid intersection problem is a classical subject in combinatorial optimization . However , only the intersection of two matroids are well…

Combinatorics · Mathematics 2023-01-10 Tianyu Liu

Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function…

Data Structures and Algorithms · Computer Science 2020-10-15 Alfredo Torrico , Mohit Singh , Sebastian Pokutta , Nika Haghtalab , Joseph , Naor , Nima Anari

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

The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…

Data Structures and Algorithms · Computer Science 2018-10-31 Nived Rajaraman , Rahul Vaze

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…

Optimization and Control · Mathematics 2016-08-30 Akhil P T , Rajesh Sundaresan

Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…

Machine Learning · Computer Science 2023-12-25 Marwa El Halabi , Jakub Tarnawski , Ashkan Norouzi-Fard , Thuy-Duong Vuong

In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…

Data Structures and Algorithms · Computer Science 2018-07-26 Sebastian Pokutta , Mohit Singh , Alfredo Torrico

In this paper we study submodular maximization under a matroid constraint in the adaptive complexity model. This model was recently introduced in the context of submodular optimization in [BS18a] to quantify the information theoretic…

Data Structures and Algorithms · Computer Science 2018-11-09 Eric Balkanski , Aviad Rubinstein , Yaron Singer

In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…

Optimization and Control · Mathematics 2023-08-07 Abhishek Roy , Geelon So , Yi-An Ma

We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…

Data Structures and Algorithms · Computer Science 2014-07-11 Gábor Ivanyos , Marek Karpinski , Nitin Saxena

This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set $E$ and $k$ weighted matroids $(E, \mathcal{I}_i, w_i)$, $i = 1, \dots, k$, and our task is to find a…

Data Structures and Algorithms · Computer Science 2017-10-04 Yasushi Kawase , Kei Kimura , Kazuhisa Makino , Hanna Sumita

Streaming submodular maximization is a natural model for the task of selecting a representative subset from a large-scale dataset. If datapoints have sensitive attributes such as gender or race, it becomes important to enforce fairness to…

Machine Learning · Computer Science 2025-11-25 Marwa El Halabi , Federico Fusco , Ashkan Norouzi-Fard , Jakab Tardos , Jakub Tarnawski

Subset selection problems ask for a small, diverse yet representative subset of the given data. When pairwise similarities are captured by a kernel, the determinants of submatrices provide a measure of diversity or independence of items…

Data Structures and Algorithms · Computer Science 2016-07-07 Tarun Kathuria , Amit Deshpande

We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…

Optimization and Control · Mathematics 2018-05-24 Chuanye Gu , Zhiyou Wu , Jueyou Li

We study the algebraic matroid induced by the ideal of (r+1)-minors of a matrix of variables over a field. This is inherently connected to the bounded-rank matrix completion problem, in which the aim is to complete a partially observed rank…

Commutative Algebra · Mathematics 2026-01-09 Lisa Nicklasson , Manolis C. Tsakiris

A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal.…

Combinatorics · Mathematics 2015-03-13 Richard P. Brent , William Orrick , Judy-anne Osborn , Paul Zimmermann

We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as…

Computer Science and Game Theory · Computer Science 2020-09-08 Vasilis Gkatzelis , Daniel Halpern , Nisarg Shah

We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…

Data Structures and Algorithms · Computer Science 2012-05-01 Yossi Azar , Iftah Gamzu