How Bad is the Freedom to Flood-It?

04/23/2018
by   Rémy Belmonte, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/28/2020

Computing Subset Transversals in H-Free Graphs

We study the computational complexity of two well-known graph transversa...
research
02/27/2023

Contracting edges to destroy a pattern: A complexity study

Given a graph G and an integer k, the objective of the Π-Contraction pro...
research
05/06/2021

Feedback Vertex Set and Even Cycle Transversal for H-Free Graphs: Finding Large Block Graphs

We prove new complexity results for Feedback Vertex Set and Even Cycle T...
research
12/10/2018

On the Enumeration Complexity of Unions of Conjunctive Queries

We study the enumeration complexity of Unions of Conjunctive Queries (UC...
research
05/10/2021

Partitioning H-Free Graphs of Bounded Diameter

A natural way of increasing our understanding of NP-complete graph probl...
research
06/22/2021

Preprocessing to Reduce the Search Space: Antler Structures for Feedback Vertex Set

The goal of this paper is to open up a new research direction aimed at u...
research
08/20/2021

The n-ary Initial Literal and Literal Shuffle

The literal and the initial literal shuffle have been introduced to mode...

Please sign up or login with your details

Forgot password? Click here to reset