English
Related papers

Related papers: Supermodular Maximization with Cardinality Constra…

200 papers

The present paper considers multipartite graphs from the perspective of design theory and coding theory. A one-factor $F$ of the complete multipartite graph $K_{n\times g}$ (with $n$ parts of size $g$) gives rise to a $(g+1)$-ary code…

Combinatorics · Mathematics 2026-02-19 Yuli Tan , Junling Zhou , Tuvi Etzion

\emph{$K$-best enumeration}, which asks to output $k$-best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been paid much…

Data Structures and Algorithms · Computer Science 2024-05-14 Kazuhiro Kurita , Kunihiro Wasa

In this paper we consider parallelization for applications whose objective can be expressed as maximizing a non-monotone submodular function under a cardinality constraint. Our main result is an algorithm whose approximation is arbitrarily…

Data Structures and Algorithms · Computer Science 2018-07-31 Eric Balkanski , Adam Breuer , Yaron Singer

We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…

Combinatorics · Mathematics 2023-05-25 Rishi Sonthalia , Anna Seigal , Guido Montufar

A $k$-submodular function is an extension of a submodular function in that its input is given by $k$ disjoint subsets instead of a single subset. For unconstrained nonnegative $k$-submodular maximization, Ward and \v{Z}ivn\'y proposed a…

Data Structures and Algorithms · Computer Science 2016-08-23 Shinsaku Sakaue

A minimum $s$-$t$ cut in a hypergraph is a bipartition of vertices that separates two nodes $s$ and $t$ while minimizing a hypergraph cut function. The cardinality-based hypergraph cut function assigns a cut penalty to each hyperedge based…

Data Structures and Algorithms · Computer Science 2024-09-25 Vedangi Bengali , Nate Veldt

We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…

Data Structures and Algorithms · Computer Science 2025-11-18 Niv Buchbinder , Joseph , Naor , David Wajc

A set $D\subseteq V$ of a graph $G=(V,E)$ is called a restrained dominating set of $G$ if every vertex not in $D$ is adjacent to a vertex in $D$ and to a vertex in $V \setminus D$. The \textsc{Minimum Restrained Domination} problem is to…

Discrete Mathematics · Computer Science 2016-06-09 Arti Pandey , B. S. Panda

Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…

Data Structures and Algorithms · Computer Science 2016-11-01 Alessandro Epasto , Silvio Lattanzi , Sergei Vassilvitskii , Morteza Zadimoghaddam

In this paper, we introduce a novel star partitioning problem for simple connected graphs $G=(V,E)$. The goal is to find a partition of the edges into stars that minimizes the maximum number of stars a node is contained in while…

Combinatorics · Mathematics 2024-08-15 Sarah Feldmann , Torben Schürenberg

Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing…

Data Structures and Algorithms · Computer Science 2024-12-04 Shuang Cui , Kai Han , Jing Tang , Xueying Li , Aakas Zhiyuli , Hanxiao Li

We study the following two fixed-cardinality optimization problems (a maximization and a minimization variant). For a fixed $\alpha$ between zero and one we are given a graph and two numbers $k \in \mathbb{N}$ and $t \in \mathbb{Q}$. The…

Data Structures and Algorithms · Computer Science 2022-10-20 Tomohiro Koana , Christian Komusiewicz , André Nichterlein , Frank Sommer

In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and…

Data Structures and Algorithms · Computer Science 2023-08-08 Yixin Chen , Alan Kuhnle

This paper considers submodular function minimization (SFM) restricted to a family of subsets. We show that SFM over complements of families with certain hierarchical structures can be solved in polynomial-time. This yields a…

Combinatorics · Mathematics 2026-03-31 Ryuhei Mizutani

A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution,…

Data Structures and Algorithms · Computer Science 2025-07-18 Chenhao Wang

We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…

Data Structures and Algorithms · Computer Science 2021-03-09 Alan Kuhnle

We study the problem of maximizing a non-monotone, non-negative submodular function subject to a matroid constraint. The prior best-known deterministic approximation ratio for this problem is $\frac{1}{4}-\epsilon$ under…

Data Structures and Algorithms · Computer Science 2020-10-23 Kai Han , Zongmai Cao , Shuang Cui , Benwei Wu

We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding…

Machine Learning · Computer Science 2019-05-28 K S Sesh Kumar , Francis Bach , Thomas Pock

Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer…

Data Structures and Algorithms · Computer Science 2016-11-01 Deeparnab Chakrabarty , Yin Tat Lee , Aaron Sidford , Sam Chiu-wai Wong

Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…

Data Structures and Algorithms · Computer Science 2015-01-26 Niv Buchbinder , Moran Feldman , Roy Schwartz