Distributed Maximization of Submodular and Approximately Submodular Functions

09/28/2020
by   Lintao Ye, et al.
0

We study the problem of maximizing a submodular function, subject to a cardinality constraint, with a set of agents communicating over a connected graph. We propose a distributed greedy algorithm that allows all the agents to converge to a near-optimal solution to the global maximization problem using only local information and communication with neighbors in the graph. The near-optimal solution approaches the (1-1/e) approximation of the optimal solution to the global maximization problem with an additive factor that depends on the number of communication steps in the algorithm. We then analyze convergence guarantees of the proposed algorithm. This analysis reveals a tradeoff between the number of communication steps and the performance of the algorithm. Finally, we extend our analysis to nonsubmodular settings, using the notion of approximate submodularity.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/23/2018

Submodular Function Maximization in Parallel via the Multilinear Relaxation

Balkanski and Singer [5] recently initiated the study of adaptivity (or ...
research
02/10/2021

Budget-Smoothed Analysis for Submodular Maximization

The greedy algorithm for submodular function maximization subject to car...
research
08/09/2018

Few Cuts Meet Many Point Sets

We study the problem of how to breakup many point sets in R^d into small...
research
02/16/2021

Unambiguous DNFs and Alon-Saks-Seymour

We exhibit an unambiguous k-DNF formula that requires CNF width Ω̃(k^2),...
research
04/07/2021

Optimal CPU Scheduling in Data Centers via a Finite-Time Distributed Quantized Coordination Mechanism

In this paper we analyze the problem of optimal task scheduling for data...
research
12/23/2020

A note on overrelaxation in the Sinkhorn algorithm

We derive an a-priori parameter range for overrelaxation of the Sinkhorn...
research
09/10/2022

The Bayan Algorithm: Detecting Communities in Networks Through Exact and Approximate Optimization of Modularity

Community detection is a classic problem in network science with extensi...

Please sign up or login with your details

Forgot password? Click here to reset