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We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a…

Machine Learning · Computer Science 2020-06-01 Anamay Chaturvedi , Huy Nguyen , Lydia Zakynthinou

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…

Data Structures and Algorithms · Computer Science 2013-08-13 Rishabh Iyer , Stefanie Jegelka , Jeff Bilmes

We study algorithms for the Submodular Multiway Partition problem (SubMP). An instance of SubMP consists of a finite ground set $V$, a subset of $k$ elements $S = \{s_1,s_2,...,s_k\}$ called terminals, and a non-negative submodular set…

Data Structures and Algorithms · Computer Science 2011-05-12 Chandra Chekuri , Alina Ene

Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…

Machine Learning · Computer Science 2019-05-07 Andrew An Bian , Baharan Mirzasoleiman , Joachim M. Buhmann , Andreas Krause

We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the…

Data Structures and Algorithms · Computer Science 2016-11-18 Wolfgang Dvořák , Monika Henzinger , David P. Williamson

Maximizing a non-negative, monontone, submodular function $f$ over $n$ elements under a cardinality constraint $k$ (SMCC) is a well-studied NP-hard problem. It has important applications in, e.g., machine learning and influence…

Data Structures and Algorithms · Computer Science 2024-02-05 Philip Cervenjak , Junhao Gan , Anthony Wirth

The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…

Data Structures and Algorithms · Computer Science 2014-08-29 Moran Feldman , Rani Izsak

Combinatorial algorithms for minimization of functions of many variables, which take their values in finite totally ordered sets, are developed. For that the decomposition of the functions by Boolean polynomials is used. The modified SFM…

Optimization and Control · Mathematics 2007-06-13 Boris Zalesky

Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…

Data Structures and Algorithms · Computer Science 2025-07-15 Moran Feldman , Alan Kuhnle

Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…

Data Structures and Algorithms · Computer Science 2019-02-20 Martin Furer , Shiva Prasad Kasiviswanathan

For a graph $G$, let $f(G)$ denote the size of the maximum cut in $G$. The problem of estimating $f(G)$ as a function of the number of vertices and edges of $G$ has a long history and was extensively studied in the last fifty years. In this…

Data Structures and Algorithms · Computer Science 2020-04-28 Charles Carlson , Alexandra Kolla , Ray Li , Nitya Mani , Benny Sudakov , Luca Trevisan

The submodular function maximization is an attractive optimization model that appears in many real applications. Although a variety of greedy algorithms quickly find good feasible solutions for many instances while guaranteeing…

Data Structures and Algorithms · Computer Science 2018-11-13 Naoya Uematsu , Shunji Umetani , Yoshinobu Kawahara

Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…

Data Structures and Algorithms · Computer Science 2020-06-25 Mehrdad Ghadiri , Richard Santiago , Bruce Shepherd

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

Data Structures and Algorithms · Computer Science 2013-04-19 Nikhil R. Devanur , Shaddin Dughmi , Roy Schwartz , Ankit Sharma , Mohit Singh

Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions…

Neural and Evolutionary Computing · Computer Science 2020-10-21 Anh Viet Do , Frank Neumann

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 $k\geq 2$ and $1\leq r\leq k$. We give an analysis of a…

Data Structures and Algorithms · Computer Science 2016-08-05 Justin Ward , Stanislav Zivny

In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that…

Optimization and Control · Mathematics 2018-02-13 Aryan Mokhtari , Hamed Hassani , Amin Karbasi

Algorithms for listing the subgraphs satisfying a given property (e.g.,being a clique, a cut, a cycle, etc.) fall within the general framework of set systems. A set system (U, F) uses a ground set U (e.g., the network nodes) and an…

Discrete Mathematics · Computer Science 2018-03-13 Alessio Conte , Roberto Grossi , Andrea Marino , Luca Versari

In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…

Machine Learning · Computer Science 2017-08-16 Hamed Hassani , Mahdi Soltanolkotabi , Amin Karbasi

Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…

Multiagent Systems · Computer Science 2009-11-13 Gagan Goel , Pushkar Tripathi , Lei Wang