Pandora’s Box Problem with Order Constraints

The Pandora’s Box problem, originally posed by Weitzman in 1979, models selection from a set of random-valued alternatives—the “boxes”—when evaluation is costly. showed that the problem admits simple threshold-based solution considers options decreasing order reservation value, proxy for actual value boxes exploration process. We study first time this when which are opened constrained, forcing to account both depth search, as opening box gives access more boxes, and breadth, there many directions explore. Despite these difficulties, we show greedy optimal strategies exist can be efficiently computed tree-like constraints. also prove finding adaptive search NP-hard approximate (up certain constant) matroid constraints applied further restrict may or given reachability on directed acyclic graph. complement hardness result giving efficient approximation algorithms, exploiting low adaptivity gap carefully relaxed version problem. Funding: This work was supported National Science Foundation [Grant 1750436] Ministero dell'Istruzione, dell'Università e della Ricerca [PRIN. ALGADIMAR “Algorithms, Games, Digital]. ERC Advanced 788893] Algorithmic Mechanism Design Research Online Markets (AMDROMA).