Metric Dimension Parameterized by Max Leaf Number

TL;DR

This paper presents a linear-time algorithm for computing the metric dimension of a graph, parameterized by the maximum number of leaves in a spanning tree, improving efficiency for certain graph classes.

Contribution

The paper introduces a new fixed-parameter algorithm for metric dimension based on the maximum leaf number, combining linear input size with a parameter-dependent function.

Findings

Algorithm runs in linear time relative to graph size.

Metric dimension can be efficiently computed for graphs with bounded maximum leaf number.

Provides a new parameterized approach to a classic graph invariant.

Abstract

The metric dimension of a graph is the size of the smallest set of vertices whose distances distinguish all pairs of vertices in the graph. We show that this graph invariant may be calculated by an algorithm whose running time is linear in the input graph size, added to a function of the largest possible number of leaves in a spanning tree of the graph.