On Grid Graph Reachability and Puzzle Games

TL;DR

This paper explores constraint programming and SAT-based methods for solving maze-like puzzle games, introducing a new reachability encoding that improves solving efficiency, especially for parallel actions.

Contribution

It proposes a novel reachability encoding for CP and SAT approaches, enhancing puzzle solving in planning as SAT frameworks.

Findings

The new encoding outperforms previous methods in solving efficiency.

Parallel action execution is significantly improved with the new encoding.

Empirical results demonstrate better scalability for complex puzzles.

Abstract

Many puzzle video games, like Sokoban, involve moving some agent in a maze. The reachable locations are usually apparent for a human player, and the difficulty of the game is mainly related to performing actions on objects, such as pushing (reachable) boxes. For this reason, the difficulty of a particular level is often measured as the number of actions on objects, other than agent walking, needed to find a solution. In this paper we study CP and SAT approaches for solving these kind of problems. We review some reachability encodings and propose a new one. We empirically show that the new encoding is well-suited for solving puzzle problems in the planning as SAT paradigm, especially when considering the execution of several actions in parallel.