Acyclic Constraint Logic and Games

Hoogeboom, Hendrik Jan; Kosters, Walter A.; Rijn, Jan N. van; Vis, Jonathan K.

doi:10.3233/icg-2014-37102

Cited by 6 publications

(3 citation statements)

References 13 publications

(22 reference statements)

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“…In the bounded length version of NCL, the orientation of each edge may be reversed at most once. This variant has been used to show NP-completeness of the games Klondike, Mahjong Solitaire and Nonogram [8]. Note that NCL gives a uniform view on games as computation and often allows for simpler proofs and strengthenings of known complexity results in this area.…”

Section: Related Workmentioning

confidence: 99%

Fixed-parameter algorithms for graph constraint logic

Hatanaka¹,

Hommelsheim

Ito

et al. 2023

Theoretical Computer Science

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Section: Related Workmentioning

confidence: 99%

Fixed-parameter algorithms for graph constraint logic

Hatanaka¹,

Hommelsheim

Ito

et al. 2023

Theoretical Computer Science

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“…Another puzzle that is similar to the Path puzzle is Nonogram, which was also proven to be NP-Complete [19,40]. Nonogram is played on a grid and requires the player to fill the cells according to the numerical clues on the side of the grid.…”

Section: Overview Of the Np-completeness Of Path Puzzlesmentioning

confidence: 99%

A Backtracking Approach for Solving Path Puzzles

Sakti,

Arzaki,

Wulandari

2023

JFMA

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We study algorithmic aspects of the Path puzzle--a logic puzzle created in 2013 and confirmed NP-complete (Non-deterministic Polynomial-time-complete) in 2020. We propose a polynomial time algorithm for verifying an arbitrary Path puzzle solution and a backtracking-based method for finding a solution to an arbitrary Path puzzle instance.To our knowledge, our study is the first rigorous investigation of an imperative algorithmic approach for solving Path puzzles. We prove that the asymptotic running time of our proposed method in solving an arbitrary Path puzzle instance of size $m \times n$ is $O(3^{mn})$. Despite this exponential upper bound, experimental results imply that a C++ implementation of our algorithm can quickly solve $6 \times 6$ Path puzzle instances in less than 30 milliseconds with an average of 3.02 milliseconds for 26 test cases. We finally prove that an $m \times n$ Path puzzle instance without row and column constraints is polynomially solvable in $O(\max\{m,n\})$ time.

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“…We will also present an engine without taking the loosely coupled subproblems into account. The game has been proven PSPACE-hard by van Rijn (2012) and Hoogeboom et al (2014).…”

mentioning

confidence: 99%

Endgame Analysis of Dou Shou Qi

Rijn¹,

Vis²

2014

ICG

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Dou Shou Qi is a game in which two players control a number of pieces, each of them aiming to move one of their pieces onto a given square. We implemented an engine for analyzing the game. Moreover, we created a series of endgame tablebases containing all configurations with up to four pieces. These tablebases are the first steps towards theoretically solving the game. Finally, we constructed decision trees based on the endgame tablebases. In this note we report on some interesting patterns.

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Acyclic Constraint Logic and Games

Cited by 6 publications

References 13 publications

Fixed-parameter algorithms for graph constraint logic

Fixed-parameter algorithms for graph constraint logic

A Backtracking Approach for Solving Path Puzzles

Endgame Analysis of Dou Shou Qi

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