Biased Pareto Optimization for Subset Selection with Dynamic Cost Constraints

TL;DR

This paper introduces BPODC, a dynamic subset selection algorithm that adapts efficiently to changing budgets while maintaining strong approximation guarantees, improving over static methods in influence maximization and coverage tasks.

Contribution

BPODC extends the POMC algorithm with biased selection and warm-up strategies, providing the first provably effective approach for dynamic cost-constrained subset selection.

Findings

BPODC maintains near-optimal approximation guarantees under budget changes.

BPODC adapts faster and more effectively than static algorithms in experiments.

BPODC's runtime is less than static greedy algorithms in dynamic scenarios.

Abstract

Subset selection with cost constraints aims to select a subset from a ground set to maximize a monotone objective function without exceeding a given budget, which has various applications such as influence maximization and maximum coverage. In real-world scenarios, the budget, representing available resources, may change over time, which requires that algorithms must adapt quickly to new budgets. However, in this dynamic environment, previous algorithms either lack theoretical guarantees or require a long running time. The state-of-the-art algorithm, POMC, is a Pareto optimization approach designed for static problems, lacking consideration for dynamic problems. In this paper, we propose BPODC, enhancing POMC with biased selection and warm-up strategies tailored for dynamic environments. We focus on the ability of BPODC to leverage existing computational results while adapting to budget changes. We prove that BPODC can maintain the best known $(\alpha_f/2)(1-e^{-\alpha_f})$-approximation guarantee when the budget changes. Experiments on influence maximization and maximum coverage show that BPODC adapts more effectively and rapidly to budget changes, with a running time that is less than that of the static greedy algorithm.