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

Marzo, Ruslán G.; Melo, Rafael A.; Ribeiro, Celso C.; Santos, Marcio Costa

doi:10.1016/j.cor.2021.105627

Cited by 5 publications

(12 citation statements)

References 27 publications

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“…A more straightforward and fair comparison between the performances of the formulations proposed in Marzo et al. (2022) and those in Bökler et al. (2020b) can be done considering the benchmarks available in PassMark (2021).…”

Section: Some Illustrative Numerical Resultsmentioning

confidence: 99%

“…The running time of CEC is only 0.2% and 10.6% of those of formulations C n int and C n,c int , respectively, for instance anna. A more straightforward and fair comparison between the performances of the formulations proposed in Marzo et al (2022) and those in Bökler et al (2020b) can be done considering the benchmarks available in PassMark (2021). The ratio 2681 2251 ≈ 1.19 between the CPU single thread ratings of the machines used in each work gives a good approximation for the relative speed between them.…”

Section: Computational Resultsmentioning

confidence: 99%

“…This section summarizes the main computational results obtained for LIPP, extracted from Marzo et al. (2022). The experiments were carried out on a machine running under Ubuntu, with an Intel(R) Core(TM) i7‐8700 Hexa‐Core 3.20 GHz and 16 GB of RAM.…”

Section: Some Illustrative Numerical Resultsmentioning

confidence: 99%

“…In this section, we review two formulations with an exponential number of constraints described in Marzo et al. (2022) for the LIPP. We also describe the clique inequalities available for problems related to finding induced subgraphs.…”

Section: The Longest Induced Path Problemmentioning

confidence: 99%

“…Remark 4. Marzo et al (2022) provided a theoretical comparison regarding the polyhedra defined by formulations CEC, CUT, and another one previously described in Bökler et al (2020aBökler et al ( , 2020b, denoted henceforth by BCWWy. They showed that the polyhedra defined by CEC and BCWWy are equivalent.…”

Section: Strengthening the Formulations With Clique Inequalitiesmentioning

confidence: 99%

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MIP formulations for induced graph optimization problems: a tutorial

Melo

Ribeiro

2023

Int Trans Operational Res

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Given a graph G=false(V,Efalse)$G=(V,E)$ and a subset of its vertices V′⊆V$V^{\prime }\subseteq V$, the subgraph induced by V′$V^{\prime }$ in G is that with vertex set V′$V^{\prime }$ and edge set E′$E^{\prime }$ formed by all the edges in E linking two vertices in V′$V^{\prime }$. Mixed integer programming (MIP) approaches are among the most successful techniques for solving induced graph optimization problems, that is, those related to obtaining maximum or minimum (weighted or not) induced subgraphs with certain properties. In this tutorial, we provide a literature review of some of these problems. Furthermore, we illustrate the use of MIP formulations and techniques for solving combinatorial optimization problems involving induced graphs. We focus on compact formulations and those with an exponential number of constraints that can be effectively solved using branch‐and‐cut procedures. More specifically, we revisit applications of their use for problems of finding induced forests (which correspond to the complement of feedback vertex sets), trees, paths, as well as quasi‐clique partitionings.

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Section: Some Illustrative Numerical Resultsmentioning

confidence: 99%

Section: Computational Resultsmentioning

confidence: 99%

Section: Some Illustrative Numerical Resultsmentioning

confidence: 99%

Section: The Longest Induced Path Problemmentioning

confidence: 99%