A heuristics approach to Hamiltonian completion problem (HCP)

Maretić, Hermina Petric; Grbic, Ante

doi:10.1109/mipro.2015.7160528

“…HCP has also been studied in the context of sparse random graphs [14]. The amount of literature that concentrates on heuristically solving HCP is more limited [26][11] [23].…”

Section: Literature Overviewmentioning

confidence: 99%

A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs

Jooken¹,

Leyman²,

Causmaecker³

2019

Preprint

0

View full text Add to dashboard Cite

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible to a given undirected graph in order to obtain a Hamiltonian graph. This problem has mainly been studied in the context of various specific kinds of undirected graphs (e.g. trees, unicyclic graphs and series-parallel graphs). The proposed algorithm, however, concentrates on solving HCP for general undirected graphs. It can be considered to belong to the category of matheuristics, because it integrates an exact linear time solution for trees into a local search algorithm for general graphs. This integration makes use of the close relation between HCP and the minimum path partition problem, which makes the algorithm equally useful for solving the latter problem. Furthermore, a benchmark set of problem instances is constructed for demonstrating the quality of the proposed algorithm. A comparison with state-of-the-art solvers indicates that the proposed algorithm is able to achieve high-quality results.

show abstract

Evolutionary operators for the Hamiltonian completion problem

Puljić

¹

,

Manger

²

2020

View full text Add to dashboard Cite

A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs

Jooken

¹

,

Leyman

²

,

Causmaecker

³

2020

View full text Add to dashboard Cite

This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible to a given undirected graph in order to obtain a Hamiltonian graph. This problem has mainly been studied in the context of various specific kinds of undirected graphs (e.g. trees, unicyclic graphs and series-parallel graphs). The proposed algorithm, however, concentrates on solving HCP for general undirected graphs. It can be considered to belong to the category of matheuristics, because it integrates an exact linear time solution for trees into a local search algorithm for general graphs. This integration makes use of the close relation between HCP and the minimum path partition problem, which makes the algorithm equally useful for solving the latter problem. Furthermore, a benchmark set of problem instances is constructed for demonstrating the quality of the proposed algorithm. A comparison with state-of-the-art solvers indicates that the proposed algorithm is able to achieve high-quality results.

show abstract

A heuristics approach to Hamiltonian completion problem (HCP)

Cited by 3 publications

References 5 publications

A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs

A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs

Evolutionary operators for the Hamiltonian completion problem

A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs

Contact Info

Product

Resources

About