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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.01244 |
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Table of Contents:
- Many popular puzzle and matching games have been analyzed through the lens of computational complexity. Prominent examples include Sudoku, Candy Crush, and Flood-It. A common theme among these widely played games is that their generalized decision versions are NP-hard, which is often thought of as a source of their inherent difficulty and addictive appeal to human players. In this paper, we study a popular single-player stacking game commonly known as Hexasort. The game can be modelled as placing colored stacks onto the vertices of a graph, where adjacent stacks of the same color merge and vanish according to deterministic rules. We prove that Hexasort is NP-hard, even when restricted to single-color stacks and progressively more constrained classes of graphs, culminating in strong NP-hardness on trees of either bounded height or degree. Towards fixed-parameter tractable algorithms, we identify settings in which the problem becomes polynomial-time solvable and present dynamic programming algorithms.