This book explores the underlying mathematical reasons for why games and puzzles are
challenging and so much fun. It shows how games and puzzles can serve as powerful …

Combinatorial games lead to several interesting, clean problems in algorithms and
complexity theory, many of which remain open. The purpose of this paper is to provide an …

We prove NP-hardness results for five of Nintendo's largest video game franchises: Mario,
Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to generalized …

We consider a graph with n vertices, and p< n pebbles of m colors. A pebble move consists
of transferring a pebble from its current host vertex to an adjacent unoccupied vertex. The …

We prove PSPACE-completeness of all but one problem in a large space of pulling-block
problems where the goal is for the agent to reach a target destination. The problems are …

The physics-based simulation game Angry Birds has been heavily researched by the AI
community over the past five years, and has been the subject of a popular AI competition …

We prove PSPACE-completeness of a broad class of moving-blocks problems similar to the
well-known puzzle Sokoban. Several computational complexity results are known for …

A pattern database (PDB) stores shortest distances from abstract states to a set of abstract
goal states. For many search problems the best heuristic function is obtained using PDBs …

Motion planning with pull moves arxiv:1008.2952v1 [cs.CC] 17 Aug 2010 Page 1 Motion
planning with pull moves Marcus Ritt ∗ It is well known that Sokoban is PSPACE-complete [3] …

This paper proves that push-pull block puzzles in 3D are PSPACE-complete to solve, and
push-pull block puzzles in 2D with thin walls are NP-hard to solve, settling an open question …