  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.
