FPT Algorithms for Conflict-free Coloring of Graphs and Chromatic Terrain Guarding

05/06/2019
by   Akanksha Agrawal, et al.
0

We present fixed parameter tractable algorithms for the conflict-free coloring problem on graphs. Given a graph G=(V,E), conflict-free coloring of G refers to coloring a subset of V such that for every vertex v, there is a color that is assigned to exactly one vertex in the closed neighborhood of v. The k-Conflict-free Coloring problem is to decide whether G can be conflict-free colored using at most k colors. This problem is NP-hard even for k=1 and therefore under standard complexity theoretic assumptions, FPT algorithms do not exist when parameterised by the solution size. We consider the k-Conflict-free Coloring problem parameterised by the treewidth of the graph and show that this problem is fixed parameter tractable. We also initiate the study of Strong Conflict-free Coloring of graphs. Given a graph G=(V,E), strong conflict-free coloring of G refers to coloring a subset of V such that every vertex v has at least one colored vertex in its closed neighborhood and moreover all the colored vertices in v's neighborhood have distinct colors. We show that this problem is in FPT when parameterised by both the treewidth and the solution size. We further apply these algorithms to get efficient algorithms for a geometric problem namely the Terrain Guarding problem, when parameterised by a structural parameter.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/22/2021

Conflict-free coloring on open neighborhoods of claw-free graphs

The `Conflict-Free Open (Closed) Neighborhood coloring', abbreviated CFO...
research
05/01/2019

Parameterized Complexity of Conflict-free Graph Coloring

Given a graph G, a q-open neighborhood conflict-free coloring or q-ONCF-...
research
04/22/2019

GLS and VNS Based Heuristics for Conflict-Free Minimum-Latency Aggregation Scheduling in WSN

We consider a conflict-free minimum latency data aggregation problem tha...
research
03/16/2023

Conflict Optimization for Binary CSP Applied to Minimum Partition into Plane Subgraphs and Graph Coloring

CG:SHOP is an annual geometric optimization challenge and the 2022 editi...
research
11/27/2018

Node Diversification in Complex Networks by Decentralized Coloring

We develop a decentralized coloring approach to diversify the nodes in a...
research
09/12/2017

Conflict-Free Coloring of Intersection Graphs

A conflict-free k-coloring of a graph G=(V,E) assigns one of k different...
research
05/18/2021

Conflict-Free Coloring: Graphs of Bounded Clique Width and Intersection Graphs

Given an undirected graph, a conflict-free coloring (CFON*) is an assign...

Please sign up or login with your details

Forgot password? Click here to reset