Twenty Years of Progress of $$\hbox {JCDCG}^3$$

Akiyama, Jin; Ito, Hiro; Sakai, Toshinori; Uno, Yushi

doi:10.1007/s00373-020-02133-4

Cited by 1 publication

(3 citation statements)

References 104 publications

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“…Cells which directly border on each other are called true neighbors. 1 Cells which are true neighbors can be gathered in a collection called a box. These boxes can consist of 1 to 4 cells.…”

Section: The Rules Of Romamentioning

confidence: 99%

“…The field of computational complexity of games and computer games is a broad vivid field as it also allows a playful entry to the field of computational complexity theory, see for instance the surveys by Demaine et al [12] and Kendall et al [30]. The importance of the field is also reflected in a huge number of publications at different international conferences over decades, such as in the conferences JCDCG3 [1] and FUN [22]. The study of games is not only a fun topic but also allows for a deeper understanding of fundamental concepts in theoretical computer science.…”

Section: Introductionmentioning

confidence: 99%

“…There are four other types of 4-boxes: , , , . A typical reasoning is: Consider cell (3,1). We cannot leave the board, which excludes .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

All Paths Lead to Rome

Goergen¹,

Fernau²,

Oest³

et al. 2022

Preprint

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All roads lead to Rome is the core idea of the puzzle game Roma. It is played on an n × n grid consisting of quadratic cells. Those cells are grouped into boxes of at most four neighboring cells and are either filled, or to be filled, with arrows pointing in cardinal directions. The goal of the game is to fill the empty cells with arrows such that each box contains at most one arrow of each direction and regardless where we start, if we follow the arrows in the cells, we will always end up in the special Roma-cell. In this work, we study the computational complexity of the puzzle game Roma and show that completing a Roma board according to the rules is an NP-complete task, counting the number of valid completions is #Pcomplete, and determining the number of preset arrows needed to make the instance uniquely solvable is Σ P 2 -complete. We further show that the problem of completing a given Roma instance on an n × n board cannot be solved in time O 2 o(n) under ETH and give a matching dynamic programming algorithm based on the idea of Catalan structures. * Supported by Deutsche Forschungsgemeinschaft (DFG), project FE560/9-1.

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Section: The Rules Of Romamentioning

confidence: 99%