English
Related papers

Related papers: Maintaining Matroid Intersections Online

200 papers

The matroid intersection problem is a fundamental problem that has been extensively studied for half a century. In the classic version of this problem, we are given two matroids $\mathcal{M}_1 = (V, \mathcal{I}_1)$ and $\mathcal{M}_2 = (V,…

Data Structures and Algorithms · Computer Science 2021-02-12 Joakim Blikstad , Jan van den Brand , Sagnik Mukhopadhyay , Danupon Nanongkai

In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…

Data Structures and Algorithms · Computer Science 2023-06-08 Chien-Chung Huang , François Sellier

Unconstrained submodular maximization captures many NP-hard combinatorial optimization problems, including Max-Cut, Max-Di-Cut, and variants of facility location problems. Recently, Buchbinder et al. presented a surprisingly simple linear…

Data Structures and Algorithms · Computer Science 2014-04-25 Norman Huang , Allan Borodin

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) recently introduced by Emek et al, (STOC 2016). This problem is defined on an underlying $n$-point metric space. An adversary presents real-time requests online…

Data Structures and Algorithms · Computer Science 2016-10-18 Yossi Azar , Ashish Chiplunkar , Haim Kaplan

In the matroid secretary problem, the elements of a matroid $\mathcal{M}$ arrive in random order. Once we observe an item we need to irrevocably decide whether or not to accept it. The set of selected elements should form an independent set…

Data Structures and Algorithms · Computer Science 2020-01-06 Mohammad Shadravan

The Matroid Secretary Problem (MSP) is one of the most prominent settings for online resource allocation and optimal stopping. A decision-maker is presented with a ground set of elements $E$ revealed sequentially and in random order. Upon…

Data Structures and Algorithms · Computer Science 2025-06-03 Kristóf Bérczi , Vasilis Livanos , José Soto , Victor Verdugo

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…

Information Theory · Computer Science 2016-11-15 Yudong Chen

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

The Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an $O(1)$-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear…

Data Structures and Algorithms · Computer Science 2023-05-10 Richard Santiago , Ivan Sergeev , Rico Zenklusen

While online bipartite matching has gained significant attention in recent years, existing analyses in stochastic settings fail to capture the performance of algorithms on heterogeneous graphs, such as those incorporating inter-group…

Data Structures and Algorithms · Computer Science 2025-06-06 Maria Cherifa , Clément Calauzènes , Vianney Perchet

Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…

Data Structures and Algorithms · Computer Science 2026-01-16 Sepideh Mahabadi , Sherry Sarkar , Jakub Tarnawski

We study the $b$-matching problem in bipartite graphs $G=(S,R,E)$. Each vertex $s\in S$ is a server with individual capacity $b_s$. The vertices $r\in R$ are requests that arrive online and must be assigned instantly to an eligible server.…

Data Structures and Algorithms · Computer Science 2022-07-01 Susanne Albers , Sebastian Schubert

The online bisection problem is a natural dynamic variant of the classic optimization problem, where one has to dynamically maintain a partition of $n$ elements into two clusters of cardinality $n/2$. During runtime, an online algorithm is…

Data Structures and Algorithms · Computer Science 2024-03-19 Marcin Bienkowski , Stefan Schmid

We give improved multi-pass streaming algorithms for the problem of maximizing a monotone or arbitrary non-negative submodular function subject to a general $p$-matchoid constraint in the model in which elements of the ground set arrive one…

Data Structures and Algorithms · Computer Science 2021-02-22 Chien-Chung Huang , Theophile Thiery , Justin Ward

Matroid intersection is a classical optimization problem where, given two matroids over the same ground set, the goal is to find the largest common independent set. In this paper, we show that there exists a certain "sparsifer": a subset of…

Data Structures and Algorithms · Computer Science 2023-10-26 Chien-Chung Huang , François Sellier

Finding a maximum cardinality common independent set in two matroids (also known as \textsc{Matroid Intersection}) is a classical combinatorial optimization problem, which generalizes several well-known problems, such as finding a maximum…

Combinatorics · Mathematics 2024-02-12 Yasuaki Kobayashi , Kazuhiro Kurita , Kunihiro Wasa

This paper presents a new research direction for the Min-cost Perfect Matching with Delays (MPMD) - a problem introduced by Emek et al. (STOC'16). In the original version of this problem, we are given an $n$-point metric space, where…

Data Structures and Algorithms · Computer Science 2025-01-07 Mathieu Mari , Michał Pawłowski , Runtian Ren , Piotr Sankowski

The control and sensing of large-scale systems results in combinatorial problems not only for sensor and actuator placement but also for scheduling or observability/controllability. Such combinatorial constraints in system design and…

Optimization and Control · Mathematics 2018-12-07 Vasileios Tzoumas , Ali Jadbabaie , George J. Pappas

Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…

Data Structures and Algorithms · Computer Science 2018-11-27 Marek Adamczyk , Michał Włodarczyk

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