License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2018.5
URN: urn:nbn:de:0030-drops-87961
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Belmonte, Rémy ; Khosravian Ghadikolaei, Mehdi ; Kiyomi, Masashi ; Lampis, Michael ; Otachi, Yota

How Bad is the Freedom to Flood-It?

LIPIcs-FUN-2018-5.pdf (0.6 MB)


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.

BibTeX - Entry

  author =	{R{\'e}my Belmonte and Mehdi Khosravian Ghadikolaei and Masashi Kiyomi and Michael Lampis and Yota Otachi},
  title =	{{How Bad is the Freedom to Flood-Itl}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Hiro Ito and Stefano Leonardi and Linda Pagli and Giuseppe Prencipe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-87961},
  doi =		{10.4230/LIPIcs.FUN.2018.5},
  annote =	{Keywords: flood-filling game, parameterized complexity}

Keywords: flood-filling game, parameterized complexity
Collection: 9th International Conference on Fun with Algorithms (FUN 2018)
Issue Date: 2018
Date of publication: 04.06.2018

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