The 2-center Problem in Maximal Outerplanar Graph

TL;DR

This paper addresses the 2-center problem in maximal outerplanar graphs, providing an $O(n^2)$ algorithm to find two centers that cover all vertices with minimal radius.

Contribution

It introduces an $O(n^2)$ time algorithm for computing the optimal 2-center and radius in maximal outerplanar graphs, improving understanding of their covering properties.

Findings

Optimal centers and radius can be computed in $O(n^2)$ time.

The graph can be partitioned into two subgraphs with continuous coverage.

The method effectively finds minimal covering radii for maximal outerplanar graphs.

Abstract

We consider the problem of computing 2-center in maximal outerplanar graph. In this problem, we want to find an optimal solution where two centers cover all the vertices with the smallest radius. We provide the following result. We can compute the optimal centers and the optimal radius in $O(n^2)$ time for a given maximal outerplanar graph with $n$ vertices. We try to let the maximal outerplanar graph be cut into two subgraphs with an internal edge, each center will cover vertices which are continuous.