A Heuristic Method of Generating Diameter 3 Graphs for Order/Degree Problem

TL;DR

This paper introduces a heuristic approach to generate large diameter 3 graphs for the order/degree problem, focusing on efficient local search and achieving optimal solutions for several cases.

Contribution

It presents a novel heuristic method tailored for large graphs with diameter 3, including an evaluation function and structure insights for improved search.

Findings

Successfully generated graphs with order > 4000 and diameter 3

Achieved best solutions for multiple graph instances

Developed an evaluation function for efficient local search

Abstract

We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the ob- servation of smaller graphs and basic structure of our heuristics. We also explain an evaluation function of each edge for efficient 2-opt local search. Using them, we found the best solutions for several graphs.