A Reduction for Optimizing Lattice Submodular Functions with Diminishing Returns

06/27/2016
by   Alina Ene, et al.
0

A function f: Z_+^E →R_+ is DR-submodular if it satisfies f( + χ_i) -f () > f( + χ_i) - f() for all <, i∈ E. Recently, the problem of maximizing a DR-submodular function f: Z_+^E →R_+ subject to a budget constraint _1 ≤ B as well as additional constraints has received significant attention SKIK14,SY15,MYK15,SY16. In this note, we give a generic reduction from the DR-submodular setting to the submodular setting. The running time of the reduction and the size of the resulting submodular instance depends only logarithmically on B. Using this reduction, one can translate the results for unconstrained and constrained submodular maximization to the DR-submodular setting for many types of constraints in a unified manner.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/29/2016

Maximizing Non-Monotone DR-Submodular Functions with Cardinality Constraints

We consider the problem of maximizing a non-monotone DR-submodular funct...
research
11/19/2021

Randomized Algorithms for Monotone Submodular Function Maximization on the Integer Lattice

Optimization problems with set submodular objective functions have many ...
research
05/18/2018

Subspace Selection via DR-Submodular Maximization on Lattices

The subspace selection problem seeks a subspace that maximizes an object...
research
02/06/2023

Jointly Optimal Routing and Caching with Bounded Link Capacities

We study a cache network in which intermediate nodes equipped with cache...
research
10/25/2022

Streaming Submodular Maximization with Differential Privacy

In this work, we study the problem of privately maximizing a submodular ...
research
11/12/2008

The Expressive Power of Binary Submodular Functions

It has previously been an open problem whether all Boolean submodular fu...
research
02/28/2017

Robust Budget Allocation via Continuous Submodular Functions

The optimal allocation of resources for maximizing influence, spread of ...

Please sign up or login with your details

Forgot password? Click here to reset