An algorithm and upper bounds for the weighted maximal planar graph problem

Ahmadi‐Javid, Amir; Ardestani-Jaafari, Amir; Foulds, L. R.; Hojabri, Hossein; Farahani, Reza Zanjirani

doi:10.1057/jors.2014.98

Cited by 7 publications

(4 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As the MWPSP is known to be strongly NP-hard [6] it should come as no surprise that exact algorithms are capable of solving general MWPSP instances with only a relatively small number of vertices [1,7] and that reported research has focused mainly on approximate and heuristic methods and the improvement of the solutions they generate [8]. The present note reports new results on solution properties and improvement strategies.…”

Section: Introductionmentioning

confidence: 83%

“…This problem is commonly formulated in terms of graph theory and is known as the maximum-weight planar subgraph problem (MWPSP). The MWPSP has some important applications: (i) as a subproblem of the plant (facility) layout problem in industrial engineering, where the vertices represent the activities of the facility and the edges the adjacencies between them in a plan of the facility [1] (ii) integrated circuit design -where the vertices are the electrical elements and the edges represent the physical connections between them [2] (iii) systems biology, where the vertices represent proteins and edges represent protein interactions in a metabolic network [3], (iv) social system analysis -where the vertices represent social agents (e.g. individuals, groups or companies) and edges represent social interaction [4], and (v) the filtering of data in correlation-based graphs in finance [5].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Results for the maximum weight planar subgraph problem

Castonguay,

Dias,

Foulds

2017

Preprint

View full text Add to dashboard Cite

The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known to be NP-hard, much research effort has been devoted over the years to attempt to improve a given approximate solution to the problem by using local moves applied to a planar embedding of the solution. It has long been established that any feasible solution to the problem, a maximal planar graph, can be transformed into any other (having the same vertex set) in a finite sequence of local moves of based on: (i) edge substitution and (ii) vertex relocation and it has been conjectured that moves of only type (i) are sufficient. In this note we settle this conjecture in the affirmative. Furthermore, contrary to recent supposition, we demonstrate that any maximal spanning tree of the original graph is not necessarily a part of any optimal solution to the problem. We hope these results will be useful in the design of future approximate methods for the problem.

show abstract

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Results for the maximum weight planar subgraph problem

Castonguay,

Dias,

Foulds

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…Zheng (2014) [81] presented a method to generate connectivity graph to contribute the facility layout generation from abstract stage. Ahmadi-Javid et al (2015) [82] recently presented a new formulation of WMPG problem using ILP model and solved it with a cutting plane algorithm.…”

Section: Fig 211 Layout Development By Graph Theorymentioning

confidence: 99%

Hopca

Çubukçuoğlu

2023

Architecture and the Built Environment

View full text Add to dashboard Cite

show abstract

“…The literature has not yet structured the potential vulnerabilities concerned with relational properties between the members of supply chain triads and has not provided a structured analytical approach towards the assessment of such vulnerabilities. We noticed that this issue could be effectively resolved using the modelling apparatus of graph theory, a mathematical approach widely adopted in operations research (e.g., Ahmadi-Javid, Ardestani-Jaafari, Foulds, Hojabri, & Farahani, 2015;Li, Kilgour, & Hipel, 2005;Ng, Cheng, Bandalouski, Kovalyov, & Lam, 2014) The aim of this study is two-fold: (i) using the toolset of graph theory, to model different cross-organizational pathways according to which risks can emerge and propagate in service triads seen as an elementary form of service supply networks; and (ii) to provide a method for vulnerability assessment of the suggested graph models of service triads, taking into consideration the typology and direction of the cross-organizational relationships within graph models of supply chain triads.…”

Section: The Application Of Graph Theory For Vulnerability Assessmentmentioning

confidence: 99%

The Application of Graph Theory for Vulnerability Assessment in Service Triads

2017

View full text Add to dashboard Cite

A supply chain triad is increasingly regarded as a unit of analysis of complex supply chain networks, allowing the realization of properties such as certain risks manifesting at the level of supply chain networks, and which are not necessarily observed at the level of supply chain dyads or individual supply chain partners. This study investigates a type of supply chain triad-service triads-and explores cross-organizational pathways according to which risks can emerge and propagate within such triadic structures. The aim of the study is to design an analytical model with the view to facilitate the assessment of vulnerability in service triads according to the aforementioned cross-organizational pathways of risk emergence and propagation. Using graph theory, a range of service triad reference models are developed, which formalize the typology and direction of the relationships between members of the supply chain triad. Adopting the notion of matrix permanent allows calculating the vulnerability levels of distinct service triad models, accounting for the formalized typology and direction of the relationships within the models. A case study in a corporate bonds context is conducted to illustrate the applicability of the proposed approach to vulnerability assessment in the service industry context.

show abstract

An algorithm and upper bounds for the weighted maximal planar graph problem

Cited by 7 publications

References 31 publications

Results for the maximum weight planar subgraph problem

Results for the maximum weight planar subgraph problem

Hopca

The Application of Graph Theory for Vulnerability Assessment in Service Triads

Contact Info

Product

Resources

About