Hardness of Metric Dimension in Graphs of Constant Treewidth

02/19/2021
by   Shaohua Li, et al.
0

The Metric Dimension problem asks for a minimum-sized resolving set in a given (unweighted, undirected) graph G. Here, a set S ⊆ V(G) is resolving if no two distinct vertices of G have the same distance vector to S. The complexity of Metric Dimension in graphs of bounded treewidth remained elusive in the past years. Recently, Bonnet and Purohit [IPEC 2019] showed that the problem is W[1]-hard under treewidth parameterization. In this work, we strengthen their lower bound to show that Metric Dimension is NP-hard in graphs of treewidth 24.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/19/2023

Metric dimension parameterized by treewidth in chordal graphs

The metric dimension has been introduced independently by Harary, Melter...
research
05/27/2018

Distributed Treewidth Computation

Of all the restricted graph families out there, the family of low treewi...
research
12/11/2012

Convex Relaxations for Learning Bounded Treewidth Decomposable Graphs

We consider the problem of learning the structure of undirected graphica...
research
05/27/2019

Hierarchy of Transportation Network Parameters and Hardness Results

The graph parameters highway dimension and skeleton dimension were intro...
research
01/10/2018

FPT algorithms for embedding into low complexity graphic metrics

The Metric Embedding problem takes as input two metric spaces (X,D_X) an...
research
09/18/2017

Localization game on geometric and planar graphs

The main topic of this paper is motivated by a localization problem in c...
research
02/09/2023

Hardness of monadic second-order formulae over succinct graphs

Our main result is a succinct counterpoint to Courcelle's meta-theorem a...

Please sign up or login with your details

Forgot password? Click here to reset