DeepAI AI Chat
Log In Sign Up

Nearly Linear-Time, Deterministic Algorithm for Maximizing (Non-Monotone) Submodular Functions Under Cardinality Constraint

by   Alan Kuhnle, et al.

A deterministic, nearly linear-time, approximation algorithm FastInterlaceGreedy is developed, for the maximization of non-monotone submodular functions under cardinality constraint. The approximation ratio of 1/4 - ε is an improvement over the next fastest deterministic algorithm for this problem, which requires quadratic time to achieve ratio 1/6 - ε. The algorithm FastInterlaceGreedy is a novel interlacing of multiple greedy procedures and is validated in the context of two applications, on which FastInterlaceGreedy outperforms the fastest deterministic and randomized algorithms in prior literature.


page 1

page 2

page 3

page 4


Streaming Algorithms for Cardinality-Constrained Maximization of Non-Monotone Submodular Functions in Linear Time

For the problem of maximizing a nonnegative, (not necessarily monotone) ...

Deterministic Approximation for Submodular Maximization over a Matroid in Nearly Linear Time

We study the problem of maximizing a non-monotone, non-negative submodul...

Simultaenous Sieves: A Deterministic Streaming Algorithm for Non-Monotone Submodular Maximization

In this work, we present a combinatorial, deterministic single-pass stre...

Submodular Optimization under Noise

We consider the problem of maximizing a monotone submodular function und...

Tight Algorithms for the Submodular Multiple Knapsack Problem

Submodular function maximization has been a central topic in the theoret...

Simultaneous Greedys: A Swiss Army Knife for Constrained Submodular Maximization

In this paper, we present SimultaneousGreedys, a deterministic algorithm...

Faster Submodular Maximization for Several Classes of Matroids

The maximization of submodular functions have found widespread applicati...