Pareto Optimization for Subset Selection with Dynamic Partition Matroid Constraints

TL;DR

This paper extends Pareto optimization methods to subset selection problems with multiple dynamic partition matroid constraints, demonstrating theoretical robustness and competitive performance against classical algorithms.

Contribution

It generalizes POMC's performance analysis from single to multiple constraints and validates its effectiveness through experiments on maxcut problems.

Findings

POMC performs competitively against GREEDY with restart.

Previous performance guarantees extend to multiple constraints.

Experimental results confirm POMC's effectiveness.

Abstract

In this study, we consider the subset selection problems with submodular or monotone discrete objective functions under partition matroid constraints where the thresholds are dynamic. We focus on POMC, a simple Pareto optimization approach that has been shown to be effective on such problems. Our analysis departs from singular constraint problems and extends to problems of multiple constraints. We show that previous results of POMC's performance also hold for multiple constraints. Our experimental investigations on random undirected maxcut problems demonstrate POMC's competitiveness against the classical GREEDY algorithm with restart strategy.