Exact and approximate algorithms for the longest induced path problem

Marzo, Ruslán G.; Ribeiro, Celso C.

doi:10.1051/ro/2021004

Cited by 5 publications

(8 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We considered in our experiments the instances proposed for the longest induced path problem in Matsypura et al (2019) and Bökler et al (2020a), also used by Marzo and Ribeiro (2021).…”

Section: Computational Experimentsmentioning

confidence: 99%

“…The warm starts used in the experiments were produced by the G-HLIPP heuristic of Marzo and Ribeiro (2021). This greedy heuristic explores all vertices of the graph as possible source vertices of induced paths.…”

Section: Experiments With More Challenging Larger Instancesmentioning

confidence: 99%

“…Furthermore, computational experiments demonstrated the superiority of the new formulations in terms of the number of instances solved to optimality and the median times for solving them. Marzo and Ribeiro (2021) proposed an exact backtracking algorithm, based on which they also derived a heuristic approach.…”

Section: Introductionmentioning

confidence: 99%

“…In the same line of the recent works of Matsypura et al (2019), Bökler et al (2020aBökler et al ( , 2020b, and Marzo and Ribeiro (2021), we consider the longest induced path problem for general graphs. We propose two new formulations with exponential numbers of constraints.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New formulations and branch-and-cut procedures for the longest induced path problem

Marzo,

Melo,

Ribeiro

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Given an undirected graph G = (V, E), the longest induced path problem (LIPP) consists of obtaining a maximum cardinality subset W ⊆ V such that W induces a simple path in G.In this paper, we propose two new formulations with an exponential number of constraints for the problem, together with effective branch-and-cut procedures for its solution. While the first formulation (cec) is based on constraints that explicitly eliminate cycles, the second one (cut) ensures connectivity via cutset constraints. We compare, both theoretically and experimentally, the newly proposed approaches with a state-of-the-art formulation recently proposed in the literature. More specifically, we show that the polyhedra defined by formulation cut and that of the formulation available in the literature are the same. Besides, we show that these two formulations are stronger in theory than cec. We also propose a new branch-andcut procedure using the new formulations. Computational experiments show that the newly proposed formulation cec, although less strong from a theoretical point of view, is the best performing approach as it can solve all but one of the 1065 benchmark instances used in the literature within the given time limit. In addition, our newly proposed approaches outperform the state-of-the-art formulation when it comes to the median times to solve the instances to optimality. Furthermore, we perform extended computational experiments considering more challenging and hard-to-solve larger instances and evaluate the impacts on the results when offering initial feasible solutions (warm starts) to the formulations.

show abstract

“…We considered in our experiments the instances proposed for the longest induced path problem in Matsypura et al (2019) and Bökler et al (2020a), also used by Marzo and Ribeiro (2021).…”

Section: Computational Experimentsmentioning

confidence: 99%

Section: Experiments With More Challenging Larger Instancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New formulations and branch-and-cut procedures for the longest induced path problem

Marzo,

Melo,

Ribeiro

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…(2019), Bökler et al. (2020), and Marzo and Ribeiro (2021) considered the problem of encountering the longest induced path. Besides, integer programming approaches have been successfully applied to several optimization problems related to encountering trees and forests with certain properties (Melo et al., 2016; Carrabs et al., 2018; Li and Aneja, 2020; Pereira et al., 2022; Carrabs et al., 2021; Labbé et al., 2021).…”

Section: Introductionmentioning

confidence: 99%

Maximum weighted induced forests and trees: new formulations and a computational comparative review

Melo

Ribeiro

2021

Int Trans Operational Res

Self Cite

View full text Add to dashboard Cite

Given a graph G=false(V,Efalse)$G=(V,E)$ with a weight wv$w_v$ associated with each vertex v∈V$v\in V$, the maximum weighted induced forest problem (MWIF) consists of encountering a maximum weighted subset V′⊆V$V^{\prime }\subseteq V$ of the vertices such that V′$V^{\prime }$ induces a forest. This NP‐hard problem is known to be equivalent to the minimum weighted feedback vertex set problem, which has applicability in a variety of domains. The closely related maximum weighted induced tree problem (MWIT), on the other hand, requires that the subset V′⊆V$V^{\prime }\subseteq V$ induces a tree. We propose two new integer programming formulations with an exponential number of constraints and branch‐and‐cut procedures for MWIF. Computational experiments using benchmark instances are performed comparing several formulations, including the newly proposed approaches and those available in the literature, when solved by a standard commercial mixed integer programming solver. More specifically, five formulations are compared, two compact ones (i.e., with a polynomial number of variables and constraints) and the three others with an exponential number of constraints. The experiments show that a new formulation for the problem based on directed cutset inequalities for eliminating cycles (DCUT) offers stronger linear relaxation bounds earlier in the search process. The results also indicate that the other new formulation, denoted tree with cycle elimination (TCYC), outperforms those available in the literature when it comes to the average times for proving optimality for the benchmark instances with up to 81 vertices. Additionally, this formulation can achieve much lower average times for solving the larger random instances that can be optimally solved. Furthermore, we show how the formulations for MWIF can be easily extended for MWIT. Such extension allowed us to analyze the difference between the optimal solution values of the two problems when considering different classes of graphs.

show abstract

New formulations and branch-and-cut procedures for the longest induced path problem

Marzo

Melo

Ribeiro

et al. 2022

Computers & Operations Research

View full text Add to dashboard Cite

Exact and approximate algorithms for the longest induced path problem

Cited by 5 publications

References 16 publications

New formulations and branch-and-cut procedures for the longest induced path problem

New formulations and branch-and-cut procedures for the longest induced path problem

Maximum weighted induced forests and trees: new formulations and a computational comparative review

New formulations and branch-and-cut procedures for the longest induced path problem

Contact Info

Product

Resources

About