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The Complexity of Flood Filling Games [article]

Raphael Clifford, Markus Jalsenius, Ashley Montanaro, Benjamin Sach
2011 arXiv   pre-print
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n by n board of tiles where each tile is allocated one of c colours.  ...  The goal is to make the colours of all tiles equal via the shortest possible sequence of flooding operations.  ...  MJ was supported by the EPSRC. We are grateful to Dave Arthur for producing an implementation of Flood-It, complete with examples of our NP-hardness reductions.  ... 
arXiv:1001.4420v3 fatcat:j33gh2usdvdf7o6tfm5gjx7u4a

The Complexity of Flood Filling Games

Raphaël Clifford, Markus Jalsenius, Ashley Montanaro, Benjamin Sach
2011 Theory of Computing Systems  
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n×n board of tiles where each tile is allocated one of c colours.  ...  The goal is to make the colours of all tiles equal via the shortest possible sequence of flooding operations.  ...  MJ was supported by the EPSRC. We are grateful to Dave Arthur for producing an implementation of Flood-It, complete with examples of our NP-hardness reductions.  ... 
doi:10.1007/s00224-011-9339-2 fatcat:6cihwzbak5hu5fmyxemdhmrdyq

The Complexity of Flood Filling Games [chapter]

David Arthur, Raphaël Clifford, Markus Jalsenius, Ashley Montanaro, Benjamin Sach
2010 Lecture Notes in Computer Science  
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n×n board of tiles where each tile is allocated one of c colours.  ...  The goal is to make the colours of all tiles equal via the shortest possible sequence of flooding operations.  ...  MJ was supported by the EPSRC. We are grateful to Dave Arthur for producing an implementation of Flood-It, complete with examples of our NP-hardness reductions.  ... 
doi:10.1007/978-3-642-13122-6_30 fatcat:yqbwez7oc5dankqnkufvfpm6rq

The complexity of flood-filling games on graphs

Kitty Meeks, Alexander Scott
2012 Discrete Applied Mathematics  
We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations  ...  Although computing the minimum number of moves required to flood an arbitrary graph is known to be NP-hard, we demonstrate a polynomial time algorithm to compute the minimum number of moves required to  ...  Introduction In this paper we consider the complexity of a number of problems related to the one-player combinatorial game Flood-It, first studied by Arthur et al. in [1] .  ... 
doi:10.1016/j.dam.2011.09.001 fatcat:ljkesgwczfgetms5xwe3sz75vi

Spanning Trees and the Complexity of Flood-Filling Games

Kitty Meeks, Alexander Scott
2013 Theory of Computing Systems  
We consider problems related to the combinatorial game (Free-)Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations.  ...  We show that the minimum number of moves required to flood any given graph G is equal to the minimum, taken over all spanning trees T of G, of the number of moves required to flood T.  ...  When the game is played on a planar graph, it can be regarded as modelling repeated use of the flood-fill tool in Microsoft Paint.  ... 
doi:10.1007/s00224-013-9482-z fatcat:xh4yve7djnefln7af46xgb6t7e

A Survey on the Complexity of Flood-Filling Games [chapter]

Michael R. Fellows, Frances A. Rosamond, Maise Dantas da Silva, Uéverton S. Souza
2018 Lecture Notes in Computer Science  
A complete mapping of the complexity of flood-filling games on trees is presented, charting the consequences of single and aggregate parameterizations.  ...  The original versions of Flood-It and Free-Flood-It are played on n × m grids, but several studies were devoted to analyzing the complexity of these games when the "board" (the graph) belongs to other  ...  Flood-Filling Games on Grids In this section we summarize the main results on the complexity of flood-filling games on grids. Theorem 1 (Clifford et al. [7] ).  ... 
doi:10.1007/978-3-319-98355-4_20 fatcat:2fxb6b5f7jdgxkiwbeei3ytsxe

Spanning Trees and the Complexity of Flood-Filling Games [chapter]

Kitty Meeks, Alexander Scott
2012 Lecture Notes in Computer Science  
We consider problems related to the combinatorial game (Free-) Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations.  ...  We show that the minimum number of moves required to flood any given graph G is equal to the minimum, taken over all spanning trees T of G, of the number of moves required to flood T .  ...  When the game is played on a planar graph, it can be regarded as modelling repeated use of the flood-fill tool in Microsoft Paint.  ... 
doi:10.1007/978-3-642-30347-0_28 fatcat:67vvpmjsmvfhbgc5azzq2qcjam

An algorithmic analysis of Flood-It and Free-Flood-It on graph powers

Uéverton dos Santos Souza, Fábio Protti, Maise Silva
2014 Discrete Mathematics & Theoretical Computer Science  
Free-Flood-it is a variant where the pivot can be freely chosen for each move of the game. The standard versions of Flood-it and Free-Flood-it are played on m ×n grids.  ...  Analysis of Algorithms International audience Flood-it is a combinatorial game played on a colored graph G whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively  ...  The main goal of this paper is to analyze the complexity of flood-filling games played on simple structures.  ... 
doi:10.46298/dmtcs.2086 fatcat:4hdsehgeivhvfhcgfvo5edibby

Algoritma Fisher-Yates Shuffle dan Flood Fill sebagai Maze Generator pada Game Labirin

D.J. Owen Hoetama, Farica Perdana Putri, P.M. Winarno
2019 Jurnal ULTIMA Computing  
Maze generator is a static level problem solution on the maze game. This research uses Fisher-Yates Shuffle algorithm and Flood Fill algorithm to make maze generator.  ...  Index Terms— Fisher-Yates Shuffle, Flood Fill, MazeGenerator, Hamming Distance  ...  Pengecekan oleh algoritma Flood Fill Hasil string setelah pengacakan akan diproses algoritma Flood Fill untuk pengecekan.  ... 
doi:10.31937/sk.v10i2.1064 fatcat:jos5g4o6jfcxbofehe757ambe4

Special Issue on Fun with Algorithms

Paolo Boldi, Luisa Gargano
2011 Theory of Computing Systems  
This is the theme of The Complexity of Flood Filling Games and Simple Wriggling is Hard unless You Are a Fat Hippo (the former about a well-known game called Flood-It, and the second considering a snake  ...  In some cases, the very inspiration of the papers come from a game or a wellknown puzzle (like in Christmas Gift Exchange Games or in The Feline Josephus Problem, that considers a generalization of a problem  ... 
doi:10.1007/s00224-011-9361-4 fatcat:viy6psmmxnhw5fi4kkrtf6jvvi

Games Ready to Use: A Serious Game for Teaching Natural Risk Management

Franck Taillandier, Carole Adam
2018 Simulation & Gaming  
In order to support risk management teaching, we propose SPRITE, an agent based serious game using a concrete case study which is exemplary in terms of risk management: the coastal floods on the Oleron  ...  and environmental issues, in a context of coastal flood risk.  ...  Game dynamics The game is based on a triple dynamic (Figure 1) : playing, flooding and election.  ... 
doi:10.1177/1046878118770217 fatcat:fs4zgzc3lraorp7abdufmbqpfq

Editorial: Fun with Algorithms

Evangelos Kranakis, Danny Krizanc, Flaminia Luccio
2013 Theory of Computing Systems  
Spanning Trees and the Complexity of Flood-Filling Games is related to the combinatorial game (Free-) Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number  ...  establishes some general schemes relating the computational complexity of a video game to the presence of certain common elements or mechanics and applies them to the analysis of several video games such  ... 
doi:10.1007/s00224-013-9503-y fatcat:62jdi54xtvb4vlyyoio6fy52vq

An Optimized Hybrid Approach for Path Finding [article]

Ahlam Ansari, Mohd Amin Sayyed, Khatija Ratlamwala, Parvin Shaikh
2015 arXiv   pre-print
The proposed algorithm can become essential part in location based, network, gaming applications. grid traversal, navigation, gaming applications, mobile robot and Artificial Intelligence.  ...  The proposed algorithm is hybrid of backtracking and a new technique(modified 8- neighbor approach).  ...  Flood fill algorithm assigns the value to each node which is represents the distance of that node from centre [9] . The flood fill algorithm floods the the maze when mouse reaches new cell or node.  ... 
arXiv:1504.02281v1 fatcat:5or5f4megvhhljjz6qxhenc4ta

An Optimized Hybrid Approach for Path Finding

Ahlam Ansari, Mohd Amin Sayyed, Khatija Ratlamwala, Parvin Shaikh
2015 International Journal in Foundations of Computer Science & Technology  
The proposed algorithm can become essential part in location based, network, gaming applications. grid traversal, navigation, gaming applications, mobile robot and Artificial Intelligence.  ...  The proposed algorithm is hybrid of backtracking and a new technique(modified 8neighbor approach).  ...  Flood fill algorithm assigns the value to each node which is represents the distance of that node from centre [9] . The flood fill algorithm floods the the maze when mouse reaches new cell or node.  ... 
doi:10.5121/ijfcst.2015.5205 fatcat:23wy4rg7xnbm3fl2cvzvnpxacu

A Narrative-Driven Role-Playing Game for Raising Flood Awareness

Fotios Spyropoulos, Ioannis Trichakis, Anthi-Eirini Vozinaki
2022 Sustainability  
In order to assess the impact of this game on participants' thoughts of who might be affected by a flood event, two questionnaires were used, one before and one after the game.  ...  awareness among the students on how floods can have an impact on the everyday lives of different citizens.  ...  A Serious Game Designed to Explore and Understand the Complexities of Flood Mitigation Options in Urban–Rural Catchments. Water 2018, 10, 1885. [CrossRef] 3. Novia, W.  ... 
doi:10.3390/su14010554 fatcat:jziiv4orzfel7emx2diosfzt7i
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