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  "path": "/abs/2602.11366v1",
  "publishedAt": "2026-02-13T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Simon Gmeiner",
    "Andreas S. Schulz"
  ],
  "textContent": "**Authors:** Simon Gmeiner, Andreas S. Schulz\n\nHow can a stack of identical blocks be arranged to extend beyond the edge of a table as far as possible? We consider a generalization of this classic puzzle to blocks that differ in width and mass. Despite the seemingly simple premise, we demonstrate that it is unlikely that one can efficiently determine a stack configuration of maximum overhang. Formally, we prove that the Block-Stacking Problem is NP-hard, partially answering an open question from the literature. Furthermore, we demonstrate that the restriction to stacks without counterweights has a surprising connection to the Airplane Refueling Problem, another famous puzzle, and to Robust Appointment Scheduling, a problem of practical relevance. In addition to revealing a remarkable relation to the real-world challenge of devising schedules under uncertainty, their equivalence unveils a polynomial-time approximation scheme, that is, a $(1+ε)$-approximation algorithm, for Block Stacking without counterbalancing and a $(2+ε)$-approximation algorithm for the general case.",
  "title": "Block Stacking, Airplane Refueling, and Robust Appointment Scheduling"
}