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How Bad is the Freedom to Flood-It?
- Source :
- Journal of Graph Algorithms and Applications, Journal of Graph Algorithms and Applications, Brown University, 2019, 23 (2), pp.111-134. ⟨10.7155/jgaa.00486⟩
- Publication Year :
- 2018
- Publisher :
- Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany, 2018.
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Abstract
- Fixed-Flood-It and Free-Flood-It are combinatorial problems on graphs that generalize a very popular puzzle called Flood-It. Both problems consist of recoloring moves whose goal is to produce a monochromatic ("flooded") graph as quickly as possible. Their difference is that in Free-Flood-It the player has the additional freedom of choosing the vertex to play in each move. In this paper, we investigate how this freedom affects the complexity of the problem. It turns out that the freedom is bad in some sense. We show that some cases trivially solvable for Fixed-Flood-It become intractable for Free-Flood-It. We also show that some tractable cases for Fixed-Flood-It are still tractable for Free-Flood-It but need considerably more involved arguments. We finally present some combinatorial properties connecting or separating the two problems. In particular, we show that the length of an optimal solution for Fixed-Flood-It is always at most twice that of Free-Flood-It, and this is tight.<br />Comment: 19 pages, 6 figures, FUN 2018
- Subjects :
- FOS: Computer and information sciences
Vertex (graph theory)
000 Computer science, knowledge, general works
General Computer Science
Computer science
Parameterized complexity
flood-filling game
Graph
Computer Science Applications
Theoretical Computer Science
Combinatorics
Computational Theory and Mathematics
Computer Science - Data Structures and Algorithms
Computer Science
Computer Science::Networking and Internet Architecture
Data Structures and Algorithms (cs.DS)
[INFO]Computer Science [cs]
Geometry and Topology
Physics::Atmospheric and Oceanic Physics
parameterized complexity
Subjects
Details
- Language :
- English
- ISSN :
- 15261719
- Database :
- OpenAIRE
- Journal :
- Journal of Graph Algorithms and Applications, Journal of Graph Algorithms and Applications, Brown University, 2019, 23 (2), pp.111-134. ⟨10.7155/jgaa.00486⟩
- Accession number :
- edsair.doi.dedup.....3007ca2f157d8b6ffad3b44dd378537e
- Full Text :
- https://doi.org/10.4230/lipics.fun.2018.5