Algorithms for the Maximum Eulerian Cycle Decomposition Problem
Abstract
Given an Eulerian graph G, in the Maximum Eulerian Cycle Decomposition problem, we are interested in finding a collection of edge-disjoint cycles {E_1, E_2, ..., E_k} in G such that all edges of G are in exactly one cycle and k is maximum. We present an algorithm to solve the pricing problem of a column generation Integer Linear Programming (ILP) model introduced by Lancia and Serafini (2016). Furthermore, we propose a greedy heuristic, which searches for minimum size cycles starting from a random vertex, and a heuristic based on partially solving the ILP model. We performed tests comparing the three approaches in relation to the quality of solutions and execution time, using distinct sets of Eulerian graphs, each set grouping graphs with different numbers of vertices and edges. Our experimental results show that the ILP based heuristic outperforms the other methods.
Keywords
Cite
@article{arxiv.2203.05446,
title = {Algorithms for the Maximum Eulerian Cycle Decomposition Problem},
author = {Pedro O. Pinheiro and Alexsandro Oliveira Alexandrino and Andre R. Oliveira and Cid C. de Souza and Zanoni Dias},
journal= {arXiv preprint arXiv:2203.05446},
year = {2022}
}