A $1\mathrm{/}2$-Approximation for Pandora's Problem with Deadlines

Pandora’s problem is a fundamental model of sequential search in which opening each box incurs a cost. We study the variant with deadlines, where each box has a publicly known deadline for both opening and selection. We prove that a simple threshold strategy achieves a $1\mathrm{/}2$-approximation to the optimal expected utility, improving the previous guarantee arbitrarily close to $1\mathrm{/}4$ due to Amanatidis et al. (2025).