Computer Science Faculty Publications and Presentations
Tile-Based Knot Assembly with Celtic!
Document Type
Conference Proceeding
Publication Date
7-15-2025
Abstract
In this paper we focus on the intersection of tile assembling systems, edge-matching puzzles, combinatorial games, and knot construction and identity. As a basis, we utilize the game Celtic!, which is a 2-Player board game where the goal of the game is to construct knots where one knot uses more of a player’s pieces than the other player over all knots. All pieces must build off an existing knot and a valid knot must be closed. We consider three variations: a 0-player self-assembly variation that deterministically places pieces to form a closed knot of some length, a 1-player puzzle variation where the goal is to form a closed knot of some length, and the original 2-player game with restricted pieces. We show these are P-complete, NP-complete (depending on the pieces), and PSPACE-complete (for a first-player win), respectively. We nearly fully characterize the hardness of the 1-player puzzle based on the pieces.
Recommended Citation
Bajaj, Divya, Ryan Knobel, Juan Manuel Perez, Rene Reyes, Ramiro Santos, and Tim Wylie. "Tile-Based Knot Assembly with Celtic!." In International Workshop on Combinatorial Algorithms, pp. 316-331. Cham: Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-98740-3_23
Publication Title
ombinatorial Algorithms. IWOCA 2025. Lecture Notes in Computer Science
DOI
10.1007/978-3-031-98740-3_23
Comments
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