A heuristic approach for dividing graphs into bi-connected components with a size constraint

TL;DR

This paper introduces a heuristic method for partitioning graphs into bi-connected components with size constraints, using an adapted open ear decomposition and local search, achieving near-optimal solutions efficiently.

Contribution

It presents a novel heuristic algorithm for the MBCPG-SC problem based on open ear decomposition and parallel growth of subgraphs, with demonstrated high-quality solutions.

Findings

Frequently finds optimal solutions

Achieves average error of a few percent

Handles graphs with up to 10,000 nodes efficiently

Abstract

In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on the open ear decomposition of graphs. Its essential part is an adaptation of the breadth first search which makes it possible to grow bi-connected subgraphs. The proposed randomized algorithm consists of growing several subgraphs in parallel. The quality of solutions generated in this way is further improved using a local search which exploits neighboring relations between the subgraphs. In order to evaluate the performance of the method, an algorithm for generating pseudo-random unit disc graphs with known optimal solutions is created. The conducted computational experiments show that the proposed method frequently manages to find optimal solutions and has an average error of only a few percent to known optimal solutions. Further, it manages to find high quality approximate solutions for graphs having up to 10.000 nodes in reasonable time.