Efficient Algorithms for Monotone Non-Submodular Maximization with Partition Matroid Constraint

TL;DR

This paper introduces efficient algorithms for maximizing monotone non-submodular functions under partition matroid constraints, providing theoretical guarantees and demonstrating superior performance in influence spread and video summarization tasks.

Contribution

It proposes novel algorithms with theoretical bounds and improved query efficiency for this class of optimization problems, along with enhanced analysis of existing methods.

Findings

Algorithms achieve comparable results to state-of-the-art with fewer queries

Theoretical bounds are established for the proposed algorithms

Applications demonstrate practical effectiveness in influence spread and video summarization

Abstract

In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition matroid constraint to (1) propose algorithms with theoretical bound and efficient query complexity; and (2) provide better analysis on theoretical performance guarantee of some existing techniques. We further investigate those algorithms' performance in two applications: Boosting Influence Spread and Video Summarization. Experiments show our algorithms return comparative results to the state-of-the-art algorithms while taking much fewer queries.